Answer
$3(2x^2+5y^2)(2x^2+5y^2)$
Work Step by Step
Factoring the $GCF=3,$ the given expression, $
12x^4-75y^4
,$ is equivalent to
\begin{align*}
&
3(4x^4-25y^4)
.\end{align*}
Using $a^2-b^2=(a+b)(a-b)$, the expression above is equivalent to
\begin{align*}\require{cancel}
&
3[(2x^2)^2-(5y^2)^2)]
\\&=
3[(2x^2+5y^2)(2x^2+5y^2)]
\\&=
3(2x^2+5y^2)(2x^2+5y^2)
.\end{align*}
Hence, the factored form of $12x^4-75y^4$ is $
3(2x^2+5y^2)(2x^2+5y^2)
$.
