Answer
$(m-4) \left( 2m+5 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Get the $GCF$ of the given expression, $
(m-4)(m+2)+(m-4)(m+3)
.$ 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 $\{
(m-4),(m-4)
\}$ is $
(m-4)
.$ Hence, the entire expression has $GCF=
(m-4)
.$
Factoring the $GCF=
(m-4)
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
(m-4) \left( \dfrac{(m-4)(m+2)}{(m-4)}+\dfrac{(m-4)(m+3)}{(m-4)} \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}
(m-4) \left( (m-4)^{1-1}(m+2)+(m-4)^{1-1}(m+3) \right)
\\\\=
(m-4) \left( (m-4)^{0}(m+2)+(m-4)^{0}(m+3) \right)
\\\\=
(m-4) \left( (1)(m+2)+(1)(m+3) \right)
\\\\=
(m-4) \left( m+2+m+3 \right)
\\\\=
(m-4) \left( 2m+5 \right)
.\end{array}