Question

What is the product of the polynomials (x2y+2)(x2−y) ?(1 point)
Responses

x4y−x2y2+2x2−2y
x superscript 4 baseline y minus x squared y squared plus 2 x squared minus 2 y

x4y−xy+x2y
x superscript 4 baseline y minus x y plus x squared y

x4y+x2−2y
x superscript 4 baseline y plus x squared minus 2 y

x3y−x2y2+2x2−2y

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). This involves multiplying each term in the first polynomial by each term in the second polynomial.

Let's distribute:

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

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 of these terms:

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

Thus, the product of the polynomials is:

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

Therefore, the correct response is:

**x4y−x2y2+2x2−2y** (x^4y - x^2y^2 + 2x^2 - 2y).