Answer
$(a+b)(3m+2b)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Factor by grouping the first $2$ and the last $2$ terms of the given expression, $
3ma+3mb+2ab+2b^2
.$ Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first $2$ and the last $2$ terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(3ma+3mb)+(2ab+2b^2)
.\end{array}
Factoring the $GCF$ in each group, results to
\begin{array}{l}\require{cancel}
3m(a+b)+2b(a+b)
.\end{array}
Factoring the $GCF=
(a+b)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(a+b)(3m+2b)
.\end{array}
