Question

What is the product of the polynomials (x^2y+2)(x^2−y) ?(1 point)
Responses

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).

Let's distribute each term in the first polynomial with each term in the second polynomial:

\[
(x^2y + 2)(x^2 - y) = x^2y \cdot x^2 + x^2y \cdot (-y) + 2 \cdot x^2 + 2 \cdot (-y)
\]

Now, let’s calculate each term separately:

1. \( x^2y \cdot x^2 = x^{4}y \)
2. \( x^2y \cdot (-y) = -x^2y^2 \)
3. \( 2 \cdot x^2 = 2x^2 \)
4. \( 2 \cdot (-y) = -2y \)

Now we can combine all the results:

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

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

\[
\boxed{x^{4}y - x^{2}y^{2} + 2x^{2} - 2y}
\]