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

Question

A) x^4y - xy + x^2y
B) x^4y + x^2 - 2y
C) x^3 - x^2y^2 + 2x^2 - 2y
D) x^4y - x^2y^2 + 2x^2 - 2y

Answer 1

To find the product of the polynomials \((x^2y + 2)(x^2 - y)\), we will use the distributive property (FOIL method). Let's distribute each term in the first polynomial across the terms in the second polynomial:

\[ (x^2y + 2)(x^2 - y) = x^2y \cdot x^2 + x^2y \cdot (-y) + 2 \cdot x^2 + 2 \cdot (-y) \]

Now calculate each term:

1. \(x^2y \cdot x^2 = x^4y\)
2. \(x^2y \cdot (-y) = -x^2y^2\)
3. \(2 \cdot x^2 = 2x^2\)
4. \(2 \cdot (-y) = -2y\)

Now, combine all the results:

\[ x^4y - x^2y^2 + 2x^2 - 2y \]

So the product of the polynomials \((x^2y + 2)(x^2 - y)\) is:

\[ x^4y - x^2y^2 + 2x^2 - 2y \]

The correct answer is:

D) \(x^4y - x^2y^2 + 2x^2 - 2y\)