Answer
$3t(5t+3)(5t-3)$
Work Step by Step
Factoring the $GCF=
3t
$, the given expression, $
75t^3-27t
,$ is equivalent to
\begin{array}{l}
3t(25t^2-9)
.\end{array}
Using $x^2-y^2=(x+y)(x-y)$ or the factoring of the difference of 2 squares, then the factored form of the expression, $
3t(25t^2-9)
,$ is
\begin{array}{l}
3t(5t+3)(5t-3)
.\end{array}