Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Section 5.1 - Greatest Common Factors and Factoring by Grouping - 5.1 Exercises: 52

Answer

$(4+m)(5+3n)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Factor by grouping the first $2$ and the last $2$ terms of the given expression, $ 20+5m+12n+3mn .$ 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} (20+5m)+(12n+3mn) .\end{array} Factoring the $GCF$ in each group, results to \begin{array}{l}\require{cancel} 5(4+m)+3n(4+m) .\end{array} Factoring the $GCF= (4+m) $ of the entire expression above results to \begin{array}{l}\require{cancel} (4+m)(5+3n) .\end{array}
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