Question

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

x3y−x2y2+2x2−2y
x cubed 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

x4y−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).

Let's distribute each term in the first polynomial:

1. **Multiply \(x^2y\) by each term in \((x^2 - y)\)**:
- \(x^2y \cdot x^2 = x^4y\)
- \(x^2y \cdot (-y) = -x^2y^2\)

2. **Multiply \(2\) by each term in \((x^2 - y)\)**:
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-y) = -2y\)

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

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

Looking at the responses you provided, the correct answer is:
\[
\boxed{x^4y - x^2y^2 + 2x^2 - 2y}
\]