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What is the product of the polynomials (x2y+2)(x2−y) ?(1 point) Responses x4y−xy+x2y x superscript 4 baseline y minus x y plus x squared y x3y−x2y2+2x2−2y x cubed y minus x squared y squared plus 2 x squared minus 2 y x4y−x2y2+2x2−2y x superscript 4 baseline y minus x squared y squared plus 2 x squared minus 2 y x4y+x2−2y

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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).

\[ (x^2y + 2)(x^2 - y) = x^2y \cdot x^2 + x^2y \cdot (-y) + 2 \cdot x^2 + 2 \cdot (-y) \]

Now, calculate each term:

  1. \(x^2y \cdot x^2 = x^{4}y\)
  2. \(x^2y \cdot (-y) = -x^2y^2\)
  3. \(2 \cdot x^2 = 2x^2\)
  4. \(2 \cdot (-y) = -2y\)

Now, combine all the terms:

\[ x^{4}y - x^{2}y^{2} + 2x^{2} - 2y \]

So the final result of the product of the polynomials \((x^2y + 2)(x^2 - y)\) is:

\[ x^{4}y - x^{2}y^{2} + 2x^{2} - 2y \]

Among the options provided, this corresponds to:

\(x^{4}y - x^{2}y^{2} + 2x^{2} - 2y\).