Table of Contents

## Algebra Mathematics

Algebra is a branch of mathematics that uses letters and symbols to represent numbers and operations. Algebra is used to solve equations and to model real-world situations.

## Basic Algebra

- Exponent
- Expression
- Polynomial (Monomial, binomial and trinomial)
- Like terms and Unlike terms
- Constants

An equation is a statement which implies two same identities separated by “=” sign. Whereas an expression is a group of different terms separated by ‘+’ or ‘-‘ sign.

Like terms are those terms whose variables and their exponents are same.

### Basic Algebra Rules

The basic algebra rules are mentioned below:

- The Symmetry rule
- The commutative rules
- The inverse of adding
- Two rules for equation

### Basic Algebra Operations

The general arithmetic operations performed in the case of algebra are:

- Addition: x + y
- Subtraction: x – y
- Multiplication: xy
- Division: x/y or x ÷ y

where x and y are the variables.

### Basic Algebra Formula

The general formulas used in algebra to solve algebraic equations and find the values of unknown variables are given here:

- a
^{2}– b^{2}= (a – b)(a + b) - (a+b)
^{2}= a^{2}+ 2ab + b^{2} - a
^{2}+ b^{2}= (a – b)^{2}+ 2ab - (a – b)
^{2}= a^{2}– 2ab + b^{2} - (a + b + c)
^{2}= a^{2}+ b^{2}+ c^{2}+ 2ab + 2ac + 2bc - (a – b – c)
^{2}= a^{2}+ b^{2}+ c^{2}– 2ab – 2ac + 2bc - (a + b)
^{3}= a^{3}+ 3a^{2}b + 3ab^{2}+ b^{3} - (a – b)
^{3}= a^{3}– 3a^{2}b + 3ab^{2}– b^{3}

### Basic Algebra Examples

**Q 1: Find y, when, y + 15 = 30**

**Solution:** y = 30 – 15

y = 15

**Q 2 : Find x, when, 9x = 63**

Ans. x = 63/9

x = 7

**Q.3: If x/7 = 21, then find x.**

Solution: Given x/7 = 21

or x = 21 x 7

x = 147

**Following Are the Rules Commonly Performed in Algebra**

1. Algebra is a type of mathematics that is used to solve equations.

2. Algebra is used to solve equations by manipulating the variables within the equation.

3. Algebra can be used to solve equations in one or more variables.

4. Algebra can be used to solve equations in two or more variables.

5. Algebra can be used to solve systems of equations.

6. Algebra can be used to solve quadratic equations.

## Important Point to Remember while Adding and Subtracting Terms

In order to add or subtract terms, one should first understand the order of operations. The order of operations is the order which operations should be completed in an equation in order to get the correct answer. The order of operations is: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

## Multiplying and Dividing Like Terms

To multiply like terms, add the coefficients of the terms to be multiplied and then multiply the terms.

To divide like terms, subtract the coefficients of the terms to be divided and then divide the terms.

Example 1

Multiply 3x + 2y and 5x – 4y

3x + 2y 5x – 4y

= 3x + 5x – 2y – 4y

= 8x – 6y

Example 2

Divide 5x + 2y by 3x

5x + 2y 3x

= 5x + 2y 3x

= 5x + 6x

= 11x