Answer
$10a^2(4m^2+1)(2m+1)(2m+1)$
Work Step by Step
Factoring the $GCF=
10a^2
$, then the given expression, $
160a^2m^4-10a^2
$ is equivalent to
\begin{array}{l}
10a^2(16m^4-1)
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, then the complete factored form of the expression above is
\begin{array}{l}
10a^2(4m^2+1)(4m^2-1)
\\\\=
10a^2(4m^2+1)(2m+1)(2m+1)
.\end{array}