# How do you factor completely 25x^2 -y^4?

$25 {x}^{2} - {y}^{4} = \left(5 x + {y}^{2}\right) \left(5 x - {y}^{2}\right)$
As $25 {x}^{2} - {y}^{4}$ is difference of two squares, to factorize it we can use the identity ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$
Hence $25 {x}^{2} - {y}^{4} = {\left(5 x\right)}^{2} - {\left({y}^{2}\right)}^{2}$
= $\left(5 x + {y}^{2}\right) \left(5 x - {y}^{2}\right)$