Answer:
the polynomial 7y²-x²y+3xy+7x²
is the additive inverse of the polynomial
-7y²+x²y-3xy-7x²
Step-by-step explanation:
Step 1:
The additive inverse of a polynomial is the polynomial that, when added to the original polynomial, results in the zero polynomial.
To find the additive inverse of the polynomial
-7y²+x²y-3xy-7x²
, we simply change the sign of every term in the polynomial. The additive inverse of this polynomial is:
7y²-x²y+3xy+7x²
Step 2:
When we add the original polynomial to its additive inverse, we get:
(-7y²+x²y-3xy-7x²)+(7y²-x²y+3xy+7x²)
Simplifying this expression, we get:
0
Therefore, the polynomial 7y²-x²y+3xy+7x² is the additive inverse of the polynomial
-7y²+x²y-3xy-7x²
.