Question

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

Explanation:

Step1: Define additive inverse

The additive inverse of a polynomial $P(x,y)$ is $-P(x,y)$, which means multiplying each term by $-1$.

Step2: Apply to given polynomial

Given polynomial: $-9xy^2 + 6x^2y - 5x^3$
Multiply each term by $-1$:
$(-1)(-9xy^2) + (-1)(6x^2y) + (-1)(-5x^3)$

Step3: Simplify each term

Calculate each product:
$9xy^2 - 6x^2y + 5x^3$

Answer:

$9xy^2 - 6x^2y + 5x^3$ (corresponding to the last option)