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 break it down step-by-step:
1. **Distribute each term in the first polynomial by each term in the second polynomial**:
- \(x^2y \cdot x^2\) gives \(x^4y\)
- \(x^2y \cdot (-y)\) gives \(-x^2y^2\)
- \(2 \cdot x^2\) gives \(2x^2\)
- \(2 \cdot (-y)\) gives \(-2y\)
2. **Combine all the terms**:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
Thus, the final product is \(x^4y - x^2y^2 + 2x^2 - 2y\).
Now let's match this with the provided options:
- \(x^4y - x^2y^2 + 2x^2 - 2y\)
This matches the fourth response option:
**x4y−x2y2+2x2−2y**.
So, the correct answer is:
**x4y−x2y2+2x2−2y**.