# How do you factor u^2 - 16v^2?

Jun 19, 2015

This is a difference of squares:

${u}^{2} - 16 {v}^{2} = {u}^{2} - {\left(4 v\right)}^{2} = \left(u - 4 v\right) \left(u + 4 v\right)$

#### Explanation:

In general ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Putting $a = u$ and $b = 4 v$ we have

${u}^{2} - 16 {v}^{2} = {u}^{2} - {\left(4 v\right)}^{2}$

$= {a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

$= \left(u - 4 v\right) \left(u + 4 v\right)$