Multiply:

To multiply, we will use distributive law as follows:

(2x2y2 − 5xy2) by (x2 − y2)

$\left(2 x^{2} y^{2}-5 x y^{2}\right)\left(x^{2}-y^{2}\right)$

$=2 x^{2} y^{2}\left(x^{2}-y^{2}\right)-5 x y^{2}\left(x^{2}-y^{2}\right)$

$=2 x^{4} y^{2}-2 x^{2} y^{4}-5 x^{3} y^{2}+5 x y^{4}$

Thus, the answer is $2 x^{4} y^{2}-2 x^{2} y^{4}-5 x^{3} y^{2}+5 x y^{4}$.