Answer
$(m+q)(x+y)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Factor by grouping the first $2$ and the last $2$ terms of the given expression, $
mx+qx+my+qy
.$ 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}
(mx+qx)+(my+qy)
.\end{array}
Factoring the $GCF$ in each group, results to
\begin{array}{l}\require{cancel}
x(m+q)+y(m+q)
.\end{array}
Factoring the $GCF=
(m+q)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(m+q)(x+y)
.\end{array}
