Answer
$(a-b)(a+b)(y-x)$
Work Step by Step
$ a^{2}y-b^{2}y-a^{2}x+b^{2}x\qquad$...factor in pairs.
$=(a^{2}y-b^{2}y)+(-a^{2}x+b^{2}x)$
$=y(a^{2}-b^{2})-x(a^{2}-b^{2})$
$=(a^{2}-b^{2})(y-x)\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=(a-b)(a+b)(y-x)$
