Answer
$-12(3x+2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Get the $GCF$ of the given expression, $
(3x+2)(x-4)-(3x+2)(x+8)
.$ 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 $\{
1,1
\}$ is $
1
.$ The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variables $\{
(3x+2),(3x+2)
\}$ is $
(3x+2)
.$ Hence, the entire expression has $GCF=
(3x+2)
.$
Factoring the $GCF=
(3x+2)
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
(3x+2) \left( \dfrac{(3x+2)(x-4)}{(3x+2)}-\dfrac{(3x+2)(x+8)}{(3x+2)} \right)
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
(3x+2) \left( (3x+2)^{1-1}(x-4)-(3x+2)^{1-1}(x+8) \right)
\\\\=
(3x+2) \left( (3x+2)^{0}(x-4)-(3x+2)^{0}(x+8) \right)
\\\\=
(3x+2) \left( (1)(x-4)-(1)(x+8) \right)
\\\\=
(3x+2) \left( x-4-x-8 \right)
\\\\=
(3x+2) \left( -12 \right)
\\\\=
-12(3x+2)
.\end{array}