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

x3y−x2y2+2x2−2y
x cubed 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

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):

1. **Multiply each term in the first polynomial by each term in the second polynomial**:

- First, distribute \( x^2y \):
1. \( x^2y \cdot x^2 = x^4y \)
2. \( x^2y \cdot (-y) = -x^2y^2 \)

- Next, distribute \( 2 \):
1. \( 2 \cdot x^2 = 2x^2 \)
2. \( 2 \cdot (-y) = -2y \)

2. **Combine all the terms** together:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

Therefore, the product of the polynomials \( (x^2y + 2)(x^2 - y) \) is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

From the options provided, the correct response is:
\[
\text{x^4y - x^2y^2 + 2x^2 - 2y}
\]