1 answer
(click or scroll down)
To find the product of the polynomials \( (x^2 y + 2)(x^2 - y) \), we will use the distributive property (also known as the FOIL method in the case of binomials) to multiply the two expressions.
1. Distribute \( x^2 y \):
\[
x^2 y \cdot x^2 = x^4 y
\]
\[
x^2 y \cdot (-y) = -x^2 y^2
\]
2. Distribute \( 2 \):
\[
2 \cdot x^2 = 2x^2
\]
\[
2 \cdot (-y) = -2y
\]
Now, combine all these results together:
\[
x^4 y - x^2 y^2 + 2x^2 - 2y
\]
Putting it all together, the product of the two polynomials is:
\[
\boxed{x^4 y - x^2 y^2 + 2x^2 - 2y}
\]