Answer
$11(2z-1)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Get the $GCF$ of the given expression, $
(2z-1)(z+6)-(2z-1)(z-5)
.$ 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 $\{
(2z-1),(2z-1)
\}$ is $
(2z-1)
.$ Hence, the entire expression has $GCF=
(2z-1)
.$
Factoring the $GCF=
(2z-1)
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
(2z-1) \left( \dfrac{(2z-1)(z+6)}{(2z-1)}-\dfrac{(2z-1)(z-5)}{(2z-1)} \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}
(2z-1) \left( (2z-1)^{1-1}(z+6)-(2z-1)^{1-1}(z-5) \right)
\\\\=
(2z-1) \left( (2z-1)^{0}(z+6)-(2z-1)^{0}(z-5) \right)
\\\\=
(2z-1) \left( (1)(z+6)-(1)(z-5) \right)
\\\\=
(2z-1) \left( z+6-z+5 \right)
\\\\=
(2z-1) \left( 11 \right)
\\\\=
11(2z-1)
.\end{array}