Answer
$-5xy \left( 6x-7y \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Get the negative $GCF$ of the given expression, $
-30x^2y+35xy^2
.$ 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 negative $GCF$ of the constants of the terms $\{
-30,35
\}$ is $
-5
$ 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 $\{
x^2y,xy^2
\}$ is $
xy
.$ Hence, the entire expression has $GCF=
-5xy
.$
Factoring the $GCF=
-5xy
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
-5xy \left( \dfrac{-30x^2y}{-5xy}+\dfrac{35xy^2}{-5xy}
\right)
\\\\=
-5xy \left( 6x-7y \right)
.\end{array}
