Answer
$8mn$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
(2m+n)^2-(2m-n)^2
,$ use the factoring of the difference of $2$ squares.
$\bf{\text{Solution Details:}}$
The expressions $
(2m+n)^2
$ and $
(2m-n)^2
$ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $
(2m+n)^2-(2m-n)^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}
[(2m+n)+(2m-n)][(2m+n)-(2m-n)]
\\\\=
(2m+n+2m-n)(2m+n-2m+n)
\\\\=
(4m)(2n)
\\\\=
8mn
.\end{array}
