Answer
$x^6y+x^4+2x^2+x^4y+1$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
(x^2+1)(x^4y+x^2+1)
,$ is
\begin{array}{l}\require{cancel}
x^2(x^4y)+x^2(x^2)+x^2(1)+1(x^4y)+1(x^2)+1(1)
\\\\=
x^6y+x^4+x^2+x^4y+x^2+1
\\\\=
x^6y+x^4+(x^2+x^2)+x^4y+1
\\\\=
x^6y+x^4+2x^2+x^4y+1
.\end{array}