# Basic Algebra Formulas

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## 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 ab and c are the leading coefficients.

The roots for this quadratic equation will be:

## 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

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: