Answer
$12(s^2+2t)(s^2-2t)$
Work Step by Step
Factoring the $GCF=12,$ the given expression, $
12s^4-48t^2
,$ is equivalent to
\begin{align*}
&
12(s^4-4t^2)
.\end{align*}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of two squares, the expression above is equivalent to
\begin{align*}
&
12[(s^2)^2-(2t)^2]
\\&=
12[(s^2+2t)(s^2-2t)]
\\&=
12(s^2+2t)(s^2-2t)
.\end{align*}
Hence, the expression $12s^4-48t^2$ is equivalent to $12(s^2+2t)(s^2-2t)$.
