Question

What is the product of the polynomials(x^2y+2)(x^2-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). We will multiply each term in the first polynomial by each term in the second polynomial.

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

2. **Distribute \(2\):**
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-y) = -2y\)

Now we combine all these products:

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

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

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