Answer
$25t^2+60t^3+36t^4$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
\left( 5t+6t^2 \right)^2
$, is equivalent to
\begin{array}{l}\require{cancel}
(5t)^2+2(5t)(6t^2)+(6t^2)^2
\\\\=
25t^2+60t^3+36t^4
.\end{array}