Answer
$3y^6-21y^4+y^3+2y^2-7y-14$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
(y^2-7)(3y^4+y+2)
,$ is
\begin{array}{l}\require{cancel}
y^2(3y^4)+y^2(y)+y^2(2)-7(3y^4)-7(y)-7(2)
\\\\=
3y^6+y^3+2y^2-21y^4-7y-14
\\\\=
3y^6-21y^4+y^3+2y^2-7y-14
.\end{array}