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
x superscript 4 baseline y plus x squared minus 2 y

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).

1. Distribute \(x^2y\) to both terms in the second polynomial:
\[
x^2y \cdot x^2 = x^4y
\]
\[
x^2y \cdot (-y) = -x^2y^2
\]

2. Distribute \(2\) to both terms in the second polynomial:
\[
2 \cdot x^2 = 2x^2
\]
\[
2 \cdot (-y) = -2y
\]

3. Now, combine all these results:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

So, the complete product is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

The correct response from the options provided is:
**x^4y − x^2y^2 + 2x^2 − 2y**.