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 in the first polynomial:
1. **Multiply \(x^2y\) by each term in \((x^2 - y)\)**:
- \(x^2y \cdot x^2 = x^4y\)
- \(x^2y \cdot (-y) = -x^2y^2\)
2. **Multiply \(2\) by each term in \((x^2 - y)\)**:
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-y) = -2y\)
Now, combine all of these results:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
Therefore, the product of the two polynomials is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
Looking at the responses you provided, the correct answer is:
\[
\boxed{x^4y - x^2y^2 + 2x^2 - 2y}
\]