## Intermediate Algebra (12th Edition)

$(n+4)(m+q)$
$\bf{\text{Solution Outline:}}$ 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}