What is the product of the polynomials (x2y+2)(x2−y)?(1 point)

Question

Responses

x4y+x2−2y
x superscript 4 baseline y plus x squared minus 2 y

x4y−xy+x2y
x superscript 4 baseline y minus x y plus x squared y

x4y−x2y2+2x2−2y
x superscript 4 baseline y minus x squared y squared plus 2 x squared minus 2 y

x3y−x2y2+2x2−2y

Answer 1

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).

Let's compute:

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

Now, let's calculate each term:

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

Now, combining all these terms together:

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

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

\[ \boxed{x^{4}y - x^{2}y^{2} + 2x^{2} - 2y} \]