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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. Distribute \(x^2y\):
- \(x^2y \cdot x^2 = x^4y\)
- \(x^2y \cdot (-y) = -x^2y^2\)
2. Distribute \(2\):
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-y) = -2y\)
Now, combine all the terms we found:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
Thus, the final expression for the product \((x^2y + 2)(x^2 - y)\) is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
From the given responses, this expression corresponds to:
\[
\text{x}^4y - \text{x}^2y^2 + 2\text{x}^2 - 2\text{y}
\]
So the correct answer is:
\[
x^3y - x^2y^2 + 2x^2 - 2y
\]
(Note: I mistakenly labeled the final combination initially, it should have been \(x^4y - x^2y^2 + 2x^2 - 2y\) which given your response items doesn't match directly, hence choose wisely based on terms.)