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). We will multiply each term in the first polynomial by each term in the second polynomial.
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Distribute \(x^2y\):
- \(x^2y \cdot x^2 = x^4y\)
- \(x^2y \cdot (-y) = -x^2y^2\)
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Distribute \(2\):
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-y) = -2y\)
Now we combine all these products:
\[ x^4y - x^2y^2 + 2x^2 - 2y \]
Thus, the product of the polynomials \((x^2y + 2)(x^2 - y)\) is:
\[ x^4y - x^2y^2 + 2x^2 - 2y \]
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