Simplify:

To simplify, we will proceed as follows:

(x2 − 2y2) (x + 4y) x2y2

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

$=\left(x^{3}+4 x^{2} y-2 x y^{2}-8 y^{3}\right) x^{2} y^{2}$

$=x^{5} y^{2}+4 x^{4} y^{3}-2 x^{3} y^{4}-8 x^{2} y^{5}$

Thus, the answer is $x^{5} y^{2}+4 x^{4} y^{3}-2 x^{3} y^{4}-8 x^{2} y^{5}$