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

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).

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

2. Distributing \(2\) through \((x^2 - y)\):
\[
2 \cdot x^2 = 2x^2
\]
\[
2 \cdot (-y) = -2y
\]

Now, we combine all these results:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

The final expression for the product \((x^2y + 2)(x^2 - y)\) is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]

Now let's compare it with the given options:
- \(x^1y + x^2 - 2y\)
- \(x^3y - x^2y^2 + 2x^2 - 2y\)
- \(x^2y - xy + x^2y\)
- \(x^2y - x^2y^2 + 2x^2 - 2y\)

The correct answer matches the last option:
\[
\text{The product is } x^4y - x^2y^2 + 2x^2 - 2y.
\]

However, it looks like there was no exact match to the product, though the closest interpretation of the expression was reflected in the fourth option. If it meant to imply that the coefficients for the highest degree in some way align, then it could be:

**Answer**: \(x^2y - x^2y^2 + 2x^2 - 2y\) (with some interpretations on degree, but actually the expected resultant polynomial is \(x^4y - x^2y^2 + 2x^2 - 2y\)).