Answer
$5x^3+x^2y-xy^2-4y^3$
Work Step by Step
Removing the grouping symbols and then combining like terms, the given expression, $
(x^3-y^3)-(-4x^3-x^2y+xy^2+3y^3)
,$ simplifies to
\begin{array}{l}\require{cancel}
x^3-y^3+4x^3+x^2y-xy^2-3y^3
\\\\=
(x^3+4x^3)+(-y^3-3y^3)+x^2y-xy^2
\\\\=
5x^3-4y^3+x^2y-xy^2
\\\\=
5x^3+x^2y-xy^2-4y^3
.\end{array}