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

Question

Responses

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−x2y2+2x2−2y
x superscript 4 baseline y minus x squared y squared plus 2 x squared minus 2 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. Distributing \(x^2y\) to each term in \((x^2 - y)\): \[ x^2y \cdot x^2 = x^4y \] \[ x^2y \cdot (-y) = -x^2y^2 \]

2. Distributing \(2\) to each term in \((x^2 - y)\): \[ 2 \cdot x^2 = 2x^2 \] \[ 2 \cdot (-y) = -2y \]

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

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

From the responses provided, the correct answer is: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

So the final answer is: x^4y - x^2y^2 + 2x^2 - 2y