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), which involves multiplying each term in the first polynomial by each term in the second polynomial.
Let's break it down:
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Multiply \(x^2y\) by each term in \(x^2 - y\): \[ x^2y \cdot x^2 = x^4y \] \[ x^2y \cdot (-y) = -x^2y^2 \]
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Now multiply \(2\) by each term in \(x^2 - y\): \[ 2 \cdot x^2 = 2x^2 \] \[ 2 \cdot (-y) = -2y \]
Now, we sum all the results together: \[ x^4y - x^2y^2 + 2x^2 - 2y \]
Thus, the product of the polynomials \((x^2y + 2)(x^2 - y)\) is: \[ \boxed{x^4y - x^2y^2 + 2x^2 - 2y} \]
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