What is the product of the polynomials (x^2y+2)(x^2−y)

Question

?(1 point)
Responses

x4y+x2−2y
x superscript 4 baseline y plus 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−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'll use the distributive property (also known as the FOIL method for binomials).

1. First, 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. Next, distribute \(2\) to both terms in the second polynomial: \[ 2 \cdot x^2 = 2x^2 \] \[ 2 \cdot (-y) = -2y \]

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

The final expression of the product is: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

From the provided options, the correct response is: x^4y - x^2y^2 + 2x^2 - 2y.