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To find the product of the polynomials \((x^2y + 2)(x^2 - y)\), we can use the distributive property (FOIL method) to expand the expression.
Let's break it down step-by-step:
1. **Distribute \(x^2y\)** across \((x^2 - y)\):
- \(x^2y \cdot x^2 = x^4y\)
- \(x^2y \cdot (-y) = -x^2y^2\)
2. **Distribute \(2\)** across \((x^2 - y)\):
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-y) = -2y\)
Now, combine all the terms from the distribution:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
So, the complete product of the polynomials \((x^2y + 2)(x^2 - y)\) is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
Among the options provided, the correct response is:
**\(x^4y - x^2y^2 + 2x^2 - 2y\)**.