The product of a + 3b and - a2 + 4ab + 2b is - a3 + xa2b + 2ab + 12ab2 + yb2. What are the values of x and y in the expression?

First, we multiply the given expressions:

(a + 3b) (-a² + 4ab + 2b)

= - a³ + 4a²b + 2ab - 3a²b + 12ab² + 6b²

Simplifying:

-a³ + a²b + 2ab + 12ab² + 6b²

By comparison, we can determine the values of x and y, which work out to be:

x = 1

b = 6