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

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).

1. Multiply each term in the first polynomial by each term in the second polynomial:
\[
(x^2y)(x^2) + (x^2y)(-y) + (2)(x^2) + (2)(-y)
\]

2. Now compute each product:
- First term: \( x^2y \cdot x^2 = x^4y \)
- Second term: \( x^2y \cdot -y = -x^2y^2 \)
- Third term: \( 2 \cdot x^2 = 2x^2 \)
- Fourth term: \( 2 \cdot -y = -2y \)

3. Combine all the products:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

Putting it all together, the product of the polynomials is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

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