Question

what is the additive inverse of the polynomial?
$-7y^{2}+x^{2}y-3xy-7x^{2}$
$\bigcirc$ $7y^{2}-x^{2}y+3xy+7x^{2}$
$\bigcirc$ $7y^{2}+x^{2}y+3xy+7x^{2}$
$\bigcirc$ $-7y^{2}-x^{2}y-3xy-7x^{2}$
$\bigcirc$ $7y^{2}+x^{2}y-3xy-7x^{2}$

Explanation:

Step1: Define additive inverse

The additive inverse of a polynomial $P$ is $-P$, which when added to $P$ gives 0.

Step2: Multiply each term by -1

$$-(-7y^2 + x^2y - 3xy - 7x^2) = (-1)(-7y^2) + (-1)(x^2y) + (-1)(-3xy) + (-1)(-7x^2)$$

Step3: Simplify each term

$$= 7y^2 - x^2y + 3xy + 7x^2$$

Answer:

A. $7y^2 - x^2y + 3xy + 7x^2$