Answer
$(a^2+b^2)(-3a+2b)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
-3a^3-3ab^2+2a^2b+2b^3
,$ such that the factored form of the groupings will result to a factor common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(-3a^3-3ab^2)+(2a^2b+2b^3)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-3a(a^2+b^2)+2b(a^2+b^2)
.\end{array}
Factoring the $GCF=
(a^2+b^2)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(a^2+b^2)(-3a+2b)
.\end{array}