# How do you factor 32x^2 – 8?

May 13, 2015

$8$ is a common factor to both the terms in the expression:

$32 {x}^{2} - 8 = 8 \left(4 {x}^{2} - 1\right)$

$= 8 \left({\left(2 x\right)}^{2} - {1}^{2}\right)$

We know that color(blue)(a^2 - b^2 = (a+b)(a-b)

Hence the above expression can be written as :

 = color(green)(8(2x+1)(2x-1)