Answer
$2(5c^3-3d)(5c^3+3d)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
