Answer
$3x^2y-2x^2y^2+2x^2y^3-7xy^3$
Work Step by Step
We remove the parentheses, distribute, and then add the products as follows
$$
xy(3x + 2xy - y^2) - 2xy^2(2x - xy + 3y)\\
=3x^2y+2x^2y^2-xy^3-4x^2y^2+2x^2y^3-6xy^3\\
=3x^2y-2x^2y^2+2x^2y^3-7xy^3
.$$
