## Intermediate Algebra: Connecting Concepts through Application

$(2m-9)(6m+11n)$
$\bf{\text{Solution Outline:}}$ To factor the given expression, $12m^2-54m+22mn-99n ,$ group the terms 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 second terms and the third and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (12m^2-54m)+(22mn-99n) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 6m(2m-9)+11n(2m-9) .\end{array} Factoring the $GCF= (2m-9)$ of the entire expression above results to \begin{array}{l}\require{cancel} (2m-9)(6m+11n) .\end{array}