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

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

x3y−x2y2+2x2−2y

Answer 1

To find the product of the polynomials \((x^2y + 2)(x^2 - y)\), we need to apply the distributive property (often referred to as the FOIL method for binomials). Here's how it works step by step:

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

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

3. Now combine all these results:
- \(x^4y - x^2y^2 + 2x^2 - 2y\)

Putting it all together, the product of the polynomials is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

Thus, the correct response is:
**x^4y − x^2y^2 + 2x^2 − 2y**