Question

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

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), which involves multiplying each term in the first polynomial by each term in the second polynomial.

Let's perform the multiplication step by step:

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

1. Multiply \( x^2y \) by \( x^2 \):
\[
x^2y \cdot x^2 = x^{2+2}y = x^4y
\]

2. Multiply \( x^2y \) by \( -y \):
\[
x^2y \cdot -y = -x^2y^2
\]

3. Multiply \( 2 \) by \( x^2 \):
\[
2 \cdot x^2 = 2x^2
\]

4. Multiply \( 2 \) by \( -y \):
\[
2 \cdot -y = -2y
\]

Now, combine all these results:

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

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

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