Intermediate Algebra: Connecting Concepts through Application

$-5xy \left( 6x-7y \right)$
$\bf{\text{Solution Outline:}}$ 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}