Answer
$15t^5-6t^4+12t^3$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
3t^2(5t^3-2t^2+4t)
,$ is
\begin{array}{l}\require{cancel}
3t^2(5t^3)-3t^2(2t^2)+3t^2(4t)
\\\\=
15t^5-6t^4+12t^3
.\end{array}