Answer
$2(4c+7d)(4c-7d)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
32c^2-98d^2
,$ factor first the $GCF.$ Then, use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
Factoring the $GCF=
2
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
2(16c^2-49d^2)
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, the factored form of the expression above is
\begin{array}{l}\require{cancel}
2(4c+7d)(4c-7d)
.\end{array}