What is the product of the polynomials(x^2y+2)(x^2-y)

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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). We will multiply each term in the first polynomial by each term in the second polynomial.

  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 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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