Answer
$(n+4)(m+q)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
4m+nq+mn+4q
,$ such that the factored form of the groupings will result to a factor that is 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 third terms and the second and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(4m+mn)+(nq+4q)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
m(4+n)+q(n+4)
\\\\=
m(n+4)+q(n+4)
.\end{array}
Factoring the $GCF=
(n+4)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(n+4)(m+q)
.\end{array}
