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

Question

Responses

x4y−x2y2+2x2−2y
x superscript 4 baseline y minus x squared y squared plus 2 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+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. Multiply each term in the first polynomial by each term in the second polynomial:

   • First, distribute \( x^2y \):

     1. \( x^2y \cdot x^2 = x^4y \)
     2. \( x^2y \cdot (-y) = -x^2y^2 \)

   • Next, distribute \( 2 \):

     1. \( 2 \cdot x^2 = 2x^2 \)
     2. \( 2 \cdot (-y) = -2y \)

2. Combine all the terms together: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

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

From the options provided, the correct response is: \[ \text{x^4y - x^2y^2 + 2x^2 - 2y} \]