# Factoring the sum of two cubes

## Statement

The sum of two cubes can be factored as follows.

$$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$

## Proof

Take $(a + b)(a^2 - ab + b^2)$ and expand the brackets. Then cancel like terms.

$$(a + b)(a^2 - ab + b^2) =$$

$$a^3 - a^2b + ab^2 + a^2b - ab^2 + b^3 =$$

$$a^3 + b^3$$