# How do you factor 16p^2-36?

Mar 20, 2016

4(2p - 3)(2p + 3 )

#### Explanation:

First 'take out' the common factor of 4.

$16 {p}^{2} - 36 = 4 \left(4 {p}^{2} - 9\right)$

now $4 {p}^{2} - 9 \text{ is a difference of squares }$

A difference of squares factors : ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

For $4 {p}^{2} - 9 , a = 2 p \text{ and } b = 3$

hence : $4 {p}^{2} - 9 = \left(2 p - 3\right) \left(2 p + 3\right)$

$\Rightarrow 16 {p}^{2} - 36 = 4 \left(2 p - 3\right) \left(2 p + 3\right)$