1 answer
(click or scroll down)
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).
Let's calculate step by step:
1. Distribute \(x^2y\) to each term in the second polynomial:
- \(x^2y \cdot x^2 = x^4y\)
- \(x^2y \cdot (-y) = -x^2y^2\)
2. Distribute \(2\) to each term in the second polynomial:
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-y) = -2y\)
Now, we combine all of these results together:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
Thus, the product of the polynomials \((x^2y + 2)(x^2 - y)\) is:
\[
x^4y - x^2y^2 + 2x^2 - 2y
\]
So the correct answer from the provided options is:
**\(x^4y - x^2y^2 + 2x^2 - 2y\)**.