Question

What is the product of the polynomials (x2y+2)(x2−y) ?(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 can use the distributive property (FOIL method) to expand the expression.

Let's break it down step-by-step:

1. Distribute \(x^2y\) across \((x^2 - y)\):

   • \(x^2y \cdot x^2 = x^4y\)
   • \(x^2y \cdot (-y) = -x^2y^2\)

2. Distribute \(2\) across \((x^2 - y)\):

   • \(2 \cdot x^2 = 2x^2\)
   • \(2 \cdot (-y) = -2y\)

Now, combine all the terms from the distribution:

\[ x^4y - x^2y^2 + 2x^2 - 2y \]

So, the complete product of the polynomials \((x^2y + 2)(x^2 - y)\) is:

\[ x^4y - x^2y^2 + 2x^2 - 2y \]

Among the options provided, the correct response is:

\(x^4y - x^2y^2 + 2x^2 - 2y\).