Question

What is the product of the polynomials (x2y+2)(x2−y)?(1 point) Responses x4y+x2−2y x superscript 4 baseline y plus x squared minus 2 y 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

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. 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 we found: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

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

From the given responses, this expression corresponds to: \[ \text{x}^4y - \text{x}^2y^2 + 2\text{x}^2 - 2\text{y} \]

So the correct answer is: \[ x^3y - x^2y^2 + 2x^2 - 2y \]

(Note: I mistakenly labeled the final combination initially, it should have been \(x^4y - x^2y^2 + 2x^2 - 2y\) which given your response items doesn't match directly, hence choose wisely based on terms.)