## Intermediate Algebra (12th Edition)

$(a+5c)(7b+1)$
$\bf{\text{Solution Outline:}}$ Group the terms of the given expression, $7ab+35bc+a+5c ,$ such that the factored form of the groupings will result to a factor 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 second terms and the third and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (7ab+35bc)+(a+5c) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 7b(a+5c)+1(a+5c) .\end{array} Factoring the $GCF= (a+5c)$ of the entire expression above results to \begin{array}{l}\require{cancel} (a+5c)(7b+1) .\end{array}