Answer
$y^6 - 1$
Work Step by Step
We multiply each term of the first polynomial by each term of the second polynomial. Then we add the products, as follows
$$
(y^5 - y^4 + y^3 - y^2 + y - 1)(y + 1)\\
=y(y^5 - y^4 + y^3 - y^2 + y - 1)+
+ (y^5 - y^4 + y^3 - y^2 + y - 1)\\
=y^6 - y^5 + y^4 - y^3 + y^2 - y
+ y^5 - y^4 + y^3 - y^2 + y - 1\\
=y^6 - 1
.$$
