Question

Multiply the polynomials and simplify: (x2y+2)(x2−y) (1 point)
Responses

x4y−x2y2+2x2−2yx to the 4th power y minus x squared y squared plus 2 x squared minus 2 y

x4y−xy+x2yx to the 4th power y minus x y plus x squared y

x4y+x2−2yx to the 4th power y plus x squared minus 2 y

x3y−x2y2+2x2−2y

Answer 1

To multiply the polynomials \((x^2y + 2)(x^2 - y)\), we can use the distributive property (also known as the FOIL method for binomials).

Here's how to do it step by step:

1. **Distribute \(x^2y\)**:
- \(x^2y \cdot x^2 = x^4y\)
- \(x^2y \cdot (-y) = -x^2y^2\)

2. **Distribute \(2\)**:
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-y) = -2y\)

Now, combine all the terms:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

So the simplified form of the polynomial multiplication \((x^2y + 2)(x^2 - y)\) is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

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