### Basic Algebra Formulas

#### Introduction

This page contains basic algebra formulas that are most commonly used. These formulas are categorized below:

### Algebra Identities

#### Difference of Squares

• a2 - b2 = (a-b)(a+b)

#### Difference of Cubes

• a3 - b3 = (a - b)(a2+ ab + b2)

#### Sum of Cubes

• a3 + b3 = (a + b)(a2 - ab + b2)

### Special Algebra Expansions

#### Formula for (a+b)2 and (a-b)2

• (a + b)2 = a2 + 2ab + b2
• (a - b)2 = a2 - 2ab +b2

#### Formula for (a+b)3 and (a-b)3

• (a + b)3 = a3 + 3a2b + 3ab2 + b3
• (a - b)3 = a3 - 3a2b + 3ab2 - b3

#### Formula

• ax2 + bx + c = 0

Where a, b and c are the leading coefficients.

The roots for this quadratic equation will be:

### Arithmetic Progression

#### Arithmetic progression

Consider the following arithmetic progression:

• a + (a + d) + (a + 2d) + (a + 3d) + ...

Where:

• a is the initial term
• d is the common difference

#### The nth term

The nth term, Tn of the arithmetic progression is:

• Tn = a + (n - 1)d

#### Sum of the first n term

The sum of the first n terms of the arithmetic progression is:

### Geometric Progression

#### Geometric progression

Consider the following geometric progression:

• a + ar + ar2 + ar3 + ...

Where:

• a is the scale factor
• r is the common ratio

#### The nth term

The nth term, Tn of the geometric progression is:

• Tn = ar n - 1

#### Sum of the first n terms

The sum of the first n terms, Sn is:

#### The sum to infinity

If -1 < r < 1, the sum to infinity, S is: