# How do you factor x^2-4y^2?

Mar 5, 2018

The factored expression is $\left(x - 2 y\right) \left(x + 2 y\right)$.

#### Explanation:

You can write the expression as a difference of squares, then use a special factoring form:

${\textcolor{red}{a}}^{2} - {\textcolor{b l u e}{b}}^{2} = \left(\textcolor{red}{a} - \textcolor{b l u e}{b}\right) \left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right)$

Here's the actual problem:

$\textcolor{w h i t e}{=} {x}^{2} - 4 {y}^{2}$

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

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

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

That's as factored as it gets.