## Intermediate Algebra: Connecting Concepts through Application

$4g \left( 3f+7 \right)$
$\bf{\text{Solution Outline:}}$ Get the $GCF$ of the given expression, $12gf+28g .$ Divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient. $\bf{\text{Solution Details:}}$ The $GCF$ of the constants of the terms $\{ 12,28 \}$ is $4$ since it is the highest number that can divide all the given constants. The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{ g,g \}$ is $g .$ Hence, the entire expression has $GCF= 4g .$ Factoring the $GCF= 4g ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 4g \left( \dfrac{12gf}{4g}+\dfrac{28g}{4g} \right) \\\\= 4g \left( 3f+7 \right) .\end{array}