Answer
$4g \left( 3f+7 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
