What is the product of the polynomials (x2y+2)(x2−y)

Question

?(1 point)
Responses

x3y−x2y2+2x2−2y
x cubed y minus x squared y squared plus 2 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

x4y+x2−2y

Answer 1

To find the product of the polynomials \((x^2y + 2)(x^2 - y)\), we need to apply the distributive property (FOIL method for binomials):

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

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

Now, let's find the final combined expression: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

The correct response is: \[ x^4y - x^2y^2 + 2x^2 - 2y \]