# How do you factor 16x^4 - 4y^2?

Jun 26, 2015

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

#### Explanation:

$16 {x}^{4} - {y}^{2}$

Factor out the GCF $4$.

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

$\left(4 {x}^{4} - {y}^{2}\right)$ is in the form of the difference of squares:

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

$a = 2 {x}^{2} \mathmr{and} b = y$

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

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