To find the additive inverse of a polynomial, you must change the sign of each term in the polynomial. Let's carefully go through each term of the polynomial \(-7y^2 + x^2y - 3xy - 7x^2\) and find its additive inverse.
### Original Polynomial
[tex]\[
-7y^2 + x^2y - 3xy - 7x^2
\][/tex]
### Steps to Find the Additive Inverse
1. Change the sign of \(-7y^2\):
The original term is \(-7y^2\). Changing the sign, it becomes:
[tex]\[
7y^2
\][/tex]
2. Change the sign of \(x^2y\):
The original term is \(x^2y\). Changing the sign, it becomes:
[tex]\[
-x^2y
\][/tex]
3. Change the sign of \(-3xy\):
The original term is \(-3xy\). Changing the sign, it becomes:
[tex]\[
3xy
\][/tex]
4. Change the sign of \(-7x^2\):
The original term is \(-7x^2\). Changing the sign, it becomes:
[tex]\[
7x^2
\][/tex]
### Additive Inverse Polynomial
Putting all the terms together, the additive inverse of the polynomial \(-7y^2 + x^2y - 3xy - 7x^2\) is:
[tex]\[
7y^2 - x^2y + 3xy + 7x^2
\][/tex]
So, the correct answer is:
[tex]\[
7 y^2 - x^2 y + 3 x y + 7 x^2
\][/tex]
