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 $(x^{2}y+2)(x^2-y)$, we will use the distributive property (also known as the FOIL method for binomials).

Let's compute:

$$(x^{2}y+2)(x^2-y)=x^{2}y\cdot x^2+x^{2}y\cdot (-y)+2\cdot x^2+2\cdot (-y)$$

Now, let's calculate each term:

1. $x^{2}y\cdot x^2=x^{4}y$
2. $x^{2}y\cdot (-y)=-x^2{y}^2$
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 $(x^{2}y+2)(x^2-y)$ is:

$$\boxed{{\displaystyle x^{4}y-x^2{y}^2+2x^2-2y}}$$