EMTeachline software - trigonometric hyperbolic identities - solutions tests

EMTask Identity Functions short

EMTeachline Mathematics Software - interactive math problem solving, test authoring

Are you a math teacher who needs a reliable cost-effective tool for preparation of tests? Are you a math student who needs detailed solutions to study for tests? If so, then you have come to the right place! EMTask offers for teachers and students a large repository of math problems with answers and solutions and easy-to-use test authoring options. Preparation of a test takes just a minute: you have to select a few topics and specify a complexity level - that's all! The software itself will select the correspoding math examples. More demanding users can select each example visually. When you save your test, EMTask automatically generates a number of similar test variants. All math tests with or without the solutions can be printed out. Dozens of tests are ready for students to review and reinforce their math skills. The trial version of EMTask can be downloaded from this site. Free online demos allow viewing variant tests and examples of math problems solutions from EMTask.

Parameters of the program

Name of program:	EMTask_Identity_Functions_short
Number of problems:	66247
Number of similar variants:	1
Languages of interface:	English, German
Price:	37 EUR
Size of archive:	5804 kb

66247 trigonometric and hyperbolic identities with solutions. Transformation, simplification, evaluation and proof of identities. All trigonometric, hyperbolic and arc-trigonometric functions included. Sorting problems by complexity levels and solution methods. Authoring options enabling development of tests, quizzes, exams and problem solving lesson plans. Automatic generation of variant tests. Dozens of ready tests.

System Requirements:

Pentium 2 or higher

64 MB RAM

Windows 98 or higher

Internet Explorer 5.5 or higher

Plug-in MathPlayer (downloadable from here)

Program's detail

●	Examples
●	Press release
●	Contents of the program
●	Characteristics of similar programs

Examples

An online sample of math problems and problem solutions from this program is provided below:

●	Problems: Hyperbolic
●	Problems: Trigonometry

EMTEACHLINE MATH TEST AUTHORING SOFTWARE - TIME-SAVING & COST-EFFECTIVE SOLUTION FOR MATH TEACHERS

Press release

ABSTRACT. EMTeachline Software has released a PC-based test authoring mathematics software package that offers a comprehensive set of test authoring tools for math teachers and a large repository of math problems in arithmetic, pre-algebra, algebra, precalculus, trigonometry and hyperbolic trigonometry, with answers and solutions. Authoring options enable teachers to select math problems by topic, difficulty level and solution method, create printable math tests, quizzes, exams and homeworks of varied complexity and develop numerous similar variants around each constructed test. The software is suitable for elementary, middle and high school use.

1. MATH SOFTWARE OVERVIEW

Teaching problem solving skills in math requires a large amount of training in solving math problems. The EMTeachline Math Test Authoring Software EMTask helps math teachers in the organization of the teaching and learning process. Provide each student in your class with an individual practice test!

The software modules are organized by subject. Each module offers hundreds of math problem types, with dozens of similar problems within one type. Math problems of 11 levels of complexity are presented in a logical sequence from basic to advanced. All problems are solved in detail.

A comprehensive set of test authoring options makes preparation of math tests, quizzes, homeworks and exams an easy and creative work. With thousands of math problems at hands, teachers do not have to search for fresh examples. They can select math problems by complexity level, solution method and type of task; develop customizable math tests of varied complexity in a minute and generate up to 30 similar variants around each constructed test. All developed materials with or without the solutions can be printed out or stored in a file and re-used. A set of variant tests is ready for students to review and reinforce their math skills.

2. MATH SKILLS COVERED

Arithmetic and Pre-Algebra: Operations: multiplication, division, addition, subtraction. Fractions, powers. Numeric expressions: estimation, equivalencies, problem-solving. Solving arithmetic problems using algebraic formulas.

Algebra: Polynomial and fractional rational expressions: transformation, simplification, evaluation. Solution of linear, quadratic, cubic, biquadratic, reciprocal and fractional algebraic equations and inequalities. Proofs of algebraic identities. Solution methods: Substitution, factoring, grouping, Bezout theorem, formulas of short multiplication, method of intervals and more.

Trigonometry and Hyperbolic Trigonometry: trigonometric and hyperbolic functions, arcus functions. Trigonometric and hyperbolic expressions: transformation, simplification, evaluation. Solution of trigonometric and hyperbolic equations. Proofs of trigonometric and hyperbolic identities. Solution methods: universal substitution, sum, product and addition of trigonometric functions, power reduction, multiple argument, shift of argument and more.

3. USER OPTIONS

For math students: You can review solutions of math problems step by step and try to solve similar math problems on your own.

For math teachers: You can use an extensive bank of math problems; arrange problems by topic, complexity level, solution method and type of task; compile math tests, quizzes, homeworks and exams of varied complexity; generate numerous similar variant math tests around a constructed example. You can use dozens of ready variant tests.

Contents of the program

Themes

Trigonometric expressions. Transformations and proofs
Hyperbolic expressions. Transformations and proofs
Trigonometric expressions. Transformations and proofs. Arcus functions

Chapters and sections

Trigonometric expressions. Transformations and proofs
Chapters	Sections
Transformation of linear expressions and expressions reduced to them	Transformation of linear expressions and expressions reduced to them. Elementary linear expressions Transformation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Transformation of linear expressions and expressions reduced to them. Linear expressions. Distributive law Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Transformation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers Transformation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Transformation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
Transformation of quadratic algebraic expressions and expressions reduced to them	Transformation of quadratic algebraic expressions and expressions reduced to them. Elementary quadratic expressions Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions containing fractions Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Decomposition of quadratic trinomial Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Grouping method Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Transformation of algebraic high-degree expressions	Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Irrational roots Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots Transformation of algebraic high-degree expressions. High degrees. Grouping method Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots Transformation of algebraic high-degree expressions. High degrees. Formulas of short multiplication Transformation of algebraic high-degree expressions. High degrees. Difference of squares Transformation of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial Transformation of algebraic high-degree expressions. High degrees. Properties of fractions Transformation of algebraic high-degree expressions. High degrees. Difference and sum of cubes Transformation of algebraic high-degree expressions. High degrees. Method of substitution
Factorization of linear expressions and expressions reduced to them	Factorization of linear expressions and expressions reduced to them. Elementary linear expressions Factorization of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Factorization of linear expressions and expressions reduced to them. Linear expressions. Distributive law Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Factorization of linear expressions and expressions reduced to them. Linear expressions. Properties of powers Factorization of linear expressions and expressions reduced to them. Expressions reduced to linear expressions Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Factorization of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
Factorization of quadratic expressions and expressions reduced to them	Factorization of quadratic expressions and expressions reduced to them. Elementary quadratic expressions Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Factorization of algebraic high-degree expressions	Factorization of algebraic high-degree expressions. High degrees. Grouping method Factorization of algebraic high-degree expressions. High degrees. Perfect square Factorization of algebraic high-degree expressions. High degrees. Difference of squares Factorization of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial Factorization of algebraic high-degree expressions. High degrees. Properties of fractions Factorization of algebraic high-degree expressions. High degrees. Difference and sum of cubes
Proof of identities related with linear expressions and expressions reduced to them	Proof of identities related with linear expressions and expressions reduced to them. Elementary linear expressions Proof of identities related with linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Distributive law Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Properties of powers Proof of identities related with linear expressions and expressions reduced to them. Expressions reduced to linear expressions Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law
Proof of identities related with quadratic expressions and expressions reduced to them	Proof of identities related with quadratic expressions and expressions reduced to them. Elementary quadratic expressions Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Proof of identities related with high-degree expressions	Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Irrational roots Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots Proof of identities related with high-degree expressions. High degrees. Grouping method Proof of identities related with high-degree expressions. High degrees. Perfect square Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots Proof of identities related with high-degree expressions. High degrees. Formulas of short multiplication Proof of identities related with high-degree expressions. High degrees. Difference of squares Proof of identities related with high-degree expressions. High degrees. Factorization of quadratic trinomial Proof of identities related with high-degree expressions. High degrees. Properties of fractions Proof of identities related with high-degree expressions. High degrees. Difference and sum of cubes Proof of identities related with high-degree expressions. High degrees. Method of substitution
Proof of identities related with fractional algebraic expressions	Proof of identities related with fractional algebraic expressions. Elementary fractional algebraic expressions Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution

Hyperbolic expressions. Transformations and proofs
Chapters	Sections
Transformation of linear expressions and expressions reduced to them	Transformation of linear expressions and expressions reduced to them. Elementary linear expressions Transformation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Transformation of linear expressions and expressions reduced to them. Linear expressions. Distributive law Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Transformation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers Transformation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Transformation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
Transformation of quadratic algebraic expressions and expressions reduced to them	Transformation of quadratic algebraic expressions and expressions reduced to them. Elementary quadratic expressions Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions containing fractions Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Decomposition of quadratic trinomial Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Grouping method Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Transformation of algebraic high-degree expressions	Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Irrational roots Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots Transformation of algebraic high-degree expressions. High degrees. Grouping method Transformation of algebraic high-degree expressions. High degrees. Perfect square Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots Transformation of algebraic high-degree expressions. High degrees. Formulas of short multiplication Transformation of algebraic high-degree expressions. High degrees. Difference of squares Transformation of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial Transformation of algebraic high-degree expressions. High degrees. Properties of fractions Transformation of algebraic high-degree expressions. High degrees. Difference and sum of cubes Transformation of algebraic high-degree expressions. High degrees. Method of substitution
Factorization of linear expressions and expressions reduced to them	Factorization of linear expressions and expressions reduced to them. Elementary linear expressions Factorization of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Factorization of linear expressions and expressions reduced to them. Linear expressions. Distributive law Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Factorization of linear expressions and expressions reduced to them. Linear expressions. Properties of powers Factorization of linear expressions and expressions reduced to them. Expressions reduced to linear expressions Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Factorization of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
Factorization of quadratic expressions and expressions reduced to them	Factorization of quadratic expressions and expressions reduced to them. Elementary quadratic expressions Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Factorization of algebraic high-degree expressions	Factorization of algebraic high-degree expressions. High degrees. Grouping method Factorization of algebraic high-degree expressions. High degrees. Perfect square Factorization of algebraic high-degree expressions. High degrees. Difference of squares Factorization of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial Factorization of algebraic high-degree expressions. High degrees. Properties of fractions Factorization of algebraic high-degree expressions. High degrees. Difference and sum of cubes
Proof of identities related with linear expressions and expressions reduced to them	Proof of identities related with linear expressions and expressions reduced to them. Elementary linear expressions Proof of identities related with linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Distributive law Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Properties of powers Proof of identities related with linear expressions and expressions reduced to them. Expressions reduced to linear expressions Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law
Proof of identities related with quadratic expressions and expressions reduced to them	Proof of identities related with quadratic expressions and expressions reduced to them. Elementary quadratic expressions Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Proof of identities related with high-degree expressions	Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Irrational roots Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots Proof of identities related with high-degree expressions. High degrees. Grouping method Proof of identities related with high-degree expressions. High degrees. Perfect square Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots Proof of identities related with high-degree expressions. High degrees. Formulas of short multiplication Proof of identities related with high-degree expressions. High degrees. Difference of squares Proof of identities related with high-degree expressions. High degrees. Factorization of quadratic trinomial Proof of identities related with high-degree expressions. High degrees. Properties of fractions Proof of identities related with high-degree expressions. High degrees. Difference and sum of cubes Proof of identities related with high-degree expressions. High degrees. Method of substitution
Proof of identities related with fractional algebraic expressions	Proof of identities related with fractional algebraic expressions. Elementary fractional algebraic expressions Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution

Trigonometric expressions. Transformations and proofs. Arcus functions
Chapters	Sections
Transformation of linear expressions and expressions reduced to them	Transformation of linear expressions and expressions reduced to them. Elementary linear expressions Transformation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Transformation of linear expressions and expressions reduced to them. Linear expressions. Distributive law Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Transformation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers Transformation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Transformation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
Transformation of quadratic algebraic expressions and expressions reduced to them	Transformation of quadratic algebraic expressions and expressions reduced to them. Elementary quadratic expressions Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions containing fractions Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Decomposition of quadratic trinomial Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Grouping method Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Transformation of algebraic high-degree expressions	Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Irrational roots Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots Transformation of algebraic high-degree expressions. High degrees. Grouping method Transformation of algebraic high-degree expressions. High degrees. Perfect square Transformation of algebraic high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots Transformation of algebraic high-degree expressions. High degrees. Formulas of short multiplication Transformation of algebraic high-degree expressions. High degrees. Difference of squares Transformation of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial Transformation of algebraic high-degree expressions. High degrees. Properties of fractions Transformation of algebraic high-degree expressions. High degrees. Difference and sum of cubes Transformation of algebraic high-degree expressions. High degrees. Method of substitution
Factorization of linear expressions and expressions reduced to them	Factorization of linear expressions and expressions reduced to them. Elementary linear expressions Factorization of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Factorization of linear expressions and expressions reduced to them. Linear expressions. Distributive law Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Factorization of linear expressions and expressions reduced to them. Linear expressions. Properties of powers Factorization of linear expressions and expressions reduced to them. Expressions reduced to linear expressions Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Factorization of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
Factorization of quadratic expressions and expressions reduced to them	Factorization of quadratic expressions and expressions reduced to them. Elementary quadratic expressions Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Factorization of algebraic high-degree expressions	Factorization of algebraic high-degree expressions. High degrees. Grouping method Factorization of algebraic high-degree expressions. High degrees. Perfect square Factorization of algebraic high-degree expressions. High degrees. Difference of squares Factorization of algebraic high-degree expressions. High degrees. Factorization of quadratic trinomial Factorization of algebraic high-degree expressions. High degrees. Properties of fractions Factorization of algebraic high-degree expressions. High degrees. Difference and sum of cubes
Proof of identities related with linear expressions and expressions reduced to them	Proof of identities related with linear expressions and expressions reduced to them. Elementary linear expressions Proof of identities related with linear expressions and expressions reduced to them. Elementary linear expressions containing fractions Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Distributive law Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Properties of powers Proof of identities related with linear expressions and expressions reduced to them. Expressions reduced to linear expressions Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients Proof of identities related with linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication Proof of identities related with linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law
Proof of identities related with quadratic expressions and expressions reduced to them	Proof of identities related with quadratic expressions and expressions reduced to them. Elementary quadratic expressions Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Rational coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients Proof of identities related with quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
Proof of identities related with high-degree expressions	Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Standard problems. Integer roots Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Irrational roots Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots Proof of identities related with high-degree expressions. High degrees. Grouping method Proof of identities related with high-degree expressions. High degrees. Perfect square Proof of identities related with high-degree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots Proof of identities related with high-degree expressions. High degrees. Formulas of short multiplication Proof of identities related with high-degree expressions. High degrees. Difference of squares Proof of identities related with high-degree expressions. High degrees. Factorization of quadratic trinomial Proof of identities related with high-degree expressions. High degrees. Properties of fractions Proof of identities related with high-degree expressions. High degrees. Difference and sum of cubes Proof of identities related with high-degree expressions. High degrees. Method of substitution
Proof of identities related with fractional algebraic expressions	Proof of identities related with fractional algebraic expressions. Elementary fractional algebraic expressions Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator Proof of identities related with fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution

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