Simplify:

To simplify, we will proceed as follows:

x2(x − y) y2(x + 2y)

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

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

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

$=x^{4} y^{2}+2 x^{3} y^{3}-\left[x^{3} y^{3}+2 x^{2} y^{4}\right]$

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

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

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