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 will use the distributive property (also known as the FOIL method for binomials).

We can expand this step by step:

1. Distribute \(x^2y\) over \((x^2 - y)\):
\[
x^2y \cdot x^2 - x^2y \cdot y = x^4y - x^2y^2
\]

2. Distribute \(2\) over \((x^2 - y)\):
\[
2 \cdot x^2 - 2 \cdot y = 2x^2 - 2y
\]

Now, we can combine all the terms together:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

So, the final product of the polynomials \((x^2y + 2)(x^2 - y)\) is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]