# Factoring the difference of two squares

## Statement

The difference of two squares can be factored as follows.

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

## Proof

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

$$(a + b)(a - b) =$$

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

$$a^2 - b^2$$

## Proofs building upon this proof

### Heron's formula: area of triangle

This shows Heron's formula for finding the area of any triangle.