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To find the product of the polynomials \((x^2y + 2)(x^2 - y)\), we will use the distributive property (FOIL method). Let's distribute each term in the first polynomial across the terms in the second polynomial:
\[
(x^2y + 2)(x^2 - y) = x^2y \cdot x^2 + x^2y \cdot (-y) + 2 \cdot x^2 + 2 \cdot (-y)
\]
Now calculate each term:
1. \(x^2y \cdot x^2 = x^4y\)
2. \(x^2y \cdot (-y) = -x^2y^2\)
3. \(2 \cdot x^2 = 2x^2\)
4. \(2 \cdot (-y) = -2y\)
Now, combine all the results:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
So the product of the polynomials \((x^2y + 2)(x^2 - y)\) is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
The correct answer is:
**D) \(x^4y - x^2y^2 + 2x^2 - 2y\)**