Answer
$3t^3+5t^2+2t+8$
Work Step by Step
Using the Distributive Property, the given expression, $
(t+2)(3t^2-t+4)
,$ is equivalent to
\begin{array}{l}\require{cancel}
t(3t^2)+t(-t)+t(4)+2(3t^2)+2(-t)+2(4)
\\\\=
3t^3-t^2+4t+6t^2-2t+8
\\\\=
3t^3+(-t^2+6t^2)+(4t-2t)+8
\\\\=
3t^3+5t^2+2t+8
.\end{array}
