## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$2(5c^3-3d)(5c^3+3d)$
$\bf{\text{Solution Outline:}}$ Get the $GCF$ of the given expression, $50c^6-18d^2 .$ Then use the factoring of the difference of $2$ squares. $\bf{\text{Solution Details:}}$ The $GCF$ of the terms is $2$ since it is the highest number that can evenly divide (no remainder) all the given terms. Factoring the $GCF,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 50c^6-18d^2 \\\\= 2(25c^6-9d^2) .\end{array} The expressions $25c^6$ and $9d^2$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $25c^6-9d^2$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2(25c^6-9d^2) \\\\= 2(5c^3-3d)(5c^3+3d) .\end{array}