Question

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−x2y2+2x2−2y x superscript 4 baseline y minus x squared y squared plus 2 x squared minus 2 y x4y−xy+x2y

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). We will multiply each term in the first polynomial by each term in the second polynomial.

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

1. First term: \( x^2y \cdot x^2 = x^4y \)
2. Outer terms: \( x^2y \cdot (-y) = -x^2y^2 \)
3. Inner terms: \( 2 \cdot x^2 = 2x^2 \)
4. Last term: \( 2 \cdot (-y) = -2y \)

Now, we will combine all of these results:

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

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

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

From your options, the matching response is:

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