Question

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

Answer 1

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:

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