Question

what is the additive inverse of the polynomial $-9xy^{2}+6x^{2}y - 5x^{3}$?
$-9xy^{2}-6x^{2}y + 5x^{3}$
$9xy^{2}+6x^{2}y + 5x^{3}$
$-9xy^{2}-6x^{2}y - 5x^{3}$
$9xy^{2}-6x^{2}y + 5x^{3}$

Explanation:

Step1: Define additive inverse

The additive inverse of a polynomial $P(x,y)$ is $-P(x,y)$, which means flipping the sign of each term.

Step2: Apply to given polynomial

Given polynomial: $-9xy^2 + 6x^2y - 5x^3$
Flip each term's sign:
$ -(-9xy^2) - (6x^2y) - (-5x^3) = 9xy^2 - 6x^2y + 5x^3 $

Answer:

$9xy^2 - 6x^2y + 5x^3$