Multiplying Polynomials Quick Check 2 of 52 of 5 Items 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). Here’s how to do it step by step:

1. Distribute \(x^2y\) to both terms in \((x^2 - y)\):

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

2. Distribute \(2\) to both terms in \((x^2 - y)\):

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

3. Now, we combine all the results:

   • From the first distribution: \(x^4y - x^2y^2\)
   • From the second distribution: \(+ 2x^2 - 2y\)

Putting it all together, we have: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

Thus, the answer in the provided choices should be: \[ x^4y - x^2y^2 + 2x^2 - 2y \]

Looking at your options, the correct response is: \[ x^3y - x^2y^2 + 2x^2 - 2y \] which appears to be a misinterpretation in exponent label, but this choice is incorrect as it shows \(x^3y\) instead of \(x^4y\).

Make sure to verify if the exact options match what you have presented. If you're looking for the precise polynomial multiplication outcome, it should be: \[ x^4y - x^2y^2 + 2x^2 - 2y \] Check it against the choices one more time!