## 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.

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

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

$$ a^2 - b^2 $$

The difference of two squares can be factored as follows.

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

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

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

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

$$ a^2 - b^2 $$

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