Answer
$16(4b+5c)(4b-5c)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
256b^2-400c^2
,$ factor first the $GCF.$ Then use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The $GCF$ of the terms in the given expression is $
16
,$ since it is the greatest expression that can divide all the terms evenly (no remainder.) Factoring the $GCF$ results to
\begin{array}{l}\require{cancel}
16(16b^2-25c^2)
.\end{array}
The expressions $
16b^2
$ and $
25c^2
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
16b^2-25c^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}
16[(4b)^2-(5c)^2]
\\\\=
16[(4b+5c)(4b-5c)]
\\\\=
16(4b+5c)(4b-5c)
.\end{array}