Answer
$15t^5-3t^4+3t^3$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $
3t^2(5t^3-t^2+t)
$, is equivalent to
\begin{array}{l}\require{cancel}
3t^2(5t^3)+3t^2(-t^2)+3t^2(t)
\\\\=
15t^5-3t^4+3t^3
.\end{array}