# Chapter 5 - Section 5.1 - Greatest Common Factors and Factoring by Grouping - 5.1 Exercises: 47

$(m+q)(x+y)$

#### 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}

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