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

Question

?(1 point)
Responses

x4y+x2−2y
x superscript 4 baseline y plus 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

x3y−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. Multiply each term in the first polynomial by each term in the second polynomial: \[ (x^2y)(x^2) + (x^2y)(-y) + (2)(x^2) + (2)(-y) \]

2. Now compute each product:

   • First term: \( x^2y \cdot x^2 = x^4y \)
   • Second term: \( x^2y \cdot -y = -x^2y^2 \)
   • Third term: \( 2 \cdot x^2 = 2x^2 \)
   • Fourth term: \( 2 \cdot -y = -2y \)

3. Combine all the products: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

Putting it all together, the product of the polynomials is: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

Therefore, the correct response is: x^4y - x^2y^2 + 2x^2 - 2y.