Question

Multiply the polynomial expression
(x^2y+2)(x^2-y)

Answer 1

To multiply the polynomial expressions \((x^2y + 2)(x^2 - y)\), we can use the distributive property (also known as the FOIL method for binomials).

We will distribute each term in the first polynomial across each term in the second polynomial:

1. Multiply \(x^2y\) by \(x^2\):
\[
x^2y \cdot x^2 = x^{4}y
\]

2. Multiply \(x^2y\) by \(-y\):
\[
x^2y \cdot (-y) = -x^2y^2
\]

3. Multiply \(2\) by \(x^2\):
\[
2 \cdot x^2 = 2x^2
\]

4. Multiply \(2\) by \(-y\):
\[
2 \cdot (-y) = -2y
\]

Now, we combine all the results:
\[
x^{4}y - x^2y^2 + 2x^2 - 2y
\]

So, the final product of the polynomial expression \((x^2y + 2)(x^2 - y)\) is:
\[
\boxed{x^{4}y - x^2y^2 + 2x^2 - 2y}
\]