# How do you factor 2x^4-32y^4?

Sep 2, 2016

$2 {x}^{4} - 32 {y}^{4} = 2 \left(x - 2 y\right) \left(x + 2 y\right) \left({x}^{2} + 4 {y}^{2}\right)$

#### Explanation:

The difference of squares identity can be written:

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

Hence we find:

$2 {x}^{4} - 32 {y}^{4} = 2 \left({x}^{4} - 16 {y}^{4}\right)$

$\textcolor{w h i t e}{2 {x}^{4} - 32 {y}^{4}} = 2 \left({\left({x}^{2}\right)}^{2} - {\left(4 {y}^{2}\right)}^{2}\right)$

$\textcolor{w h i t e}{2 {x}^{4} - 32 {y}^{4}} = 2 \left({x}^{2} - 4 {y}^{2}\right) \left({x}^{2} + 4 {y}^{2}\right)$

$\textcolor{w h i t e}{2 {x}^{4} - 32 {y}^{4}} = 2 \left({x}^{2} - {\left(2 y\right)}^{2}\right) \left({x}^{2} + 4 {y}^{2}\right)$

$\textcolor{w h i t e}{2 {x}^{4} - 32 {y}^{4}} = 2 \left(x - 2 y\right) \left(x + 2 y\right) \left({x}^{2} + 4 {y}^{2}\right)$