**Basic Algebra Formulas**

**Algebra Identities**

**Difference of Squares**

**a**^{2} – b^{2} = (a-b)(a+b)

^{2}– b

^{2}= (a-b)(a+b)

#### Difference of Cubes

**a**^{3} – b^{3} = (a – b)(a^{2}+ ab + b^{2})

^{3}– b

^{3}= (a – b)(a

^{2}+ ab + b

^{2})

#### Sum of Cubes

**a**^{3} + b^{3} = (a + b)(a^{2} – ab + b^{2})

^{3}+ b

^{3}= (a + b)(a

^{2}– ab + b

^{2})

**Special Algebra Expansions**

Formula for (a+b)

^{2}and (a-b)^{2}**(a + b)**^{2} = a^{2} + 2ab + b^{2}

^{2}= a

^{2}+ 2ab + b

^{2}

**(a – b)**^{2} = a^{2} – 2ab +b^{2}

^{2}= a

^{2}– 2ab +b

^{2}

#### Formula for (a+b)^{3} and (a-b)^{3}

**(a + b)**^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

^{3}= a

^{3}+ 3a

^{2}b + 3ab

^{2}+ b

^{3}

**(a – b)**^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}

^{3}= a

^{3}– 3a

^{2}b + 3ab

^{2}– b

^{3}

**Roots of Quadratic Equation**

#### Formula

#### Consider this quadratic equation:

**ax**^{2} + bx + c = 0

^{2}+ bx + c = 0

#### Where a, b 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 n^{th} term

#### The n^{th} term, T_{n} of the arithmetic progression is:

**T**_{n} = a + (n – 1)d

_{n}= 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 + ar**^{2} + ar^{3} + …

^{2}+ ar

^{3}+ …

#### Where:

#### a is the scale factor

#### r is the common ratio

#### The n^{th} term

#### The n^{th} term, T_{n} of the geometric progression is:

**T**_{n} = ar ^{n – 1}

_{n}= ar

^{n – 1}