Question

What is the additive inverse of the polynomial –9xy2 + 6x2y – 5x3

Answer 1

9xy2-6x2y+5x3.  Change every sign in the equation as if you were multiplying each part by -1.

Answer 2

Answer:  The required additive inverse of the given polynomial is $9xy^2-6x^2y+5x^3.$

Step-by-step explanation:  We are given to find the additive inverse of the following polynomial :

$P=-9xy^2+6x^2y-5x^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let Q be the polynomial that represents the additive inverse of the polynomial P.

Then, the sum of the polynomials P and  must be zero.

That is,

$P+Q=0\\\\\Rightarrow (-9xy^2+6x^2y-5x^3)+Q=0\\\\\Rightarrow Q=0-(-9xy^2+6x^2y-5x^3)\\\\\Rightarrow Q=0+9xy^2-6x^2y+5x^3\\\\\Rightarrow Q=9xy^2-6x^2y+5x^3.$

Thus, the required additive inverse of the given polynomial is $9xy^2-6x^2y+5x^3.$