# Basic Identities in Algebra

### Distributive Law

#### a(b + c) = ab + ac

### Commutative Law

#### a + b = b + a

### Associative Law

#### (a + b) + c = a + (b + c)

### Difference of Squares

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

### Sum of Cubes

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

### Difference of Cubes

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