Answer
$-6t^3-3t^2+2t+1$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of $2$ binomials, the given expression, $
(1+2t)(1-3t^2)
$, is equivalent to
\begin{array}{l}\require{cancel}
1(1)+1(-3t^2)+2t(1)+2t(-3t^2)
\\\\=
1-3t^2+2t-6t^3
\\\\=
-6t^3-3t^2+2t+1
.\end{array}
