Answer
$25-20t^3+4t^6$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
\left( 5-2t^3 \right)^2
$, is equivalent to
\begin{array}{l}\require{cancel}
(5)^2+2(5)(-2t^3)+(-2t^3)^2
\\\\=
25-20t^3+4t^6
.\end{array}