# How do you factor x^2 - y^2 ?

Jul 7, 2015

This is known as a difference of squares.

It can be factored as: ${x}^{2} - {y}^{2} = \left(x - y\right) \left(x + y\right)$

#### Explanation:

Notice that when you multiply $\left(x - y\right)$ by $\left(x + y\right)$ then the terms in $x y$ cancel out, leaving ${x}^{2} - {y}^{2}$ ...

$\left(x - y\right) \left(x + y\right) = {x}^{2} + x y - y x - {y}^{2}$

$= {x}^{2} + x y - x y - {y}^{2}$

$= {x}^{2} - {y}^{2}$

In general, if you spot something in the form ${a}^{2} - {b}^{2}$ then it can be factored as $\left(a - b\right) \left(a + b\right)$

For example:

$9 {x}^{2} - 16 {y}^{2} = {\left(3 x\right)}^{2} - {\left(4 y\right)}^{2} = \left(3 x - 4 y\right) \left(3 x + 4 y\right)$