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

To find the product of the polynomials \( (x^2 y + 2)(x^2 - y) \), we will use the distributive property (also known as the FOIL method in the case of binomials) to multiply the two expressions.

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

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

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

Putting it all together, the product of the two polynomials is:
\[
\boxed{x^4 y - x^2 y^2 + 2x^2 - 2y}
\]