What is the product of the polynomials (x2y+2)(x2−y)?(1 point)

To find the product of the polynomials \((x^2y+2)(x^2−y)\), we can use the distributive property (also known as the FOIL method for binomials).

Let's distribute each term from the first polynomial to each term in the second polynomial:

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

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, combine all these results:

\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

Thus, the product of the polynomials \((x^2y+2)(x^2−y)\) is:

\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

Therefore, the correct response is:
**\(x^4y - x^2y^2 + 2x^2 - 2y\)**.