To find the product of the polynomials \((x^2y + 2)(x^2 - y)\), you can use the distributive property (also known as the FOIL method for binomials).
Here’s how you can do it step-by-step:
-
Distribute each term in the first polynomial to each term in the second polynomial:
\[ (x^2y + 2)(x^2 - y) = x^2y \cdot x^2 + x^2y \cdot (-y) + 2 \cdot x^2 + 2 \cdot (-y) \]
-
Calculate each of the products:
- \(x^2y \cdot x^2 = x^{2+2}y = x^4y\)
- \(x^2y \cdot (-y) = -x^2y^2\)
- \(2 \cdot x^2 = 2x^2\)
- \(2 \cdot (-y) = -2y\)
-
Combine all these results:
\[ x^4y - x^2y^2 + 2x^2 - 2y \]
Therefore, the product of the polynomials \((x^2y + 2)(x^2 - y)\) is:
\[ x^4y - x^2y^2 + 2x^2 - 2y \]