Respuesta :
9xy2-6x2y+5x3. Change every sign in the equation as if you were multiplying each part by -1.
Answer: The required additive inverse of the given polynomial is [tex]9xy^2-6x^2y+5x^3.[/tex]
Step-by-step explanation: We are given to find the additive inverse of the following polynomial :
[tex]P=-9xy^2+6x^2y-5x^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
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,
[tex]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.[/tex]
Thus, the required additive inverse of the given polynomial is [tex]9xy^2-6x^2y+5x^3.[/tex]
