Answer
(x +y) (x - y)(x +2y) (x -2 y)
Work Step by Step
$x^{4}$ - 5$x^{2}$$y^{2}$ + 4$y^{4}$
= $x^{4}$ - 4$x^{2}$$y^{2}$ - $x^{2}$$y^{2}$ + 4$y^{4}$
= $x^{2}$( $x^{2}$- 4$y^{2}$) - $y^{2}$($x^{2}$ - 4$y^{2}$)
= ($x^{2}$ - $y^{2}$) ($x^{2}$ - 4$y^{2}$)
Now apply {($x^{2}$ - $y^{2}$) = (x +y) (x - y)} in both polynomials
($x^{2}$ - $y^{2}$) ($x^{2}$ - 4$y^{2}$) = (x +y) (x - y)(x +2y) (x -2 y)
So final answer: (x +y) (x - y)(x +2y) (x -2 y)
