Answer: The result would be - 2x^2 + 3xy + 8y^2.
Explanation:
(-x^2 + 9xy) - (x^2 + 6xy - 8y^2)
The objective of this question is to remove the brackets.
The first pair of brackets could simply be removed since it won't need changing (because it's positive, without symbols in front). As for the second one, we must remove the brackets in some way, which is to make basically every term in that bracket the negative of the 'original' ones.
The negative of x^2 = - x^2
The negative of + 6xy = - 6xy
The negative of - 8y^2 = + 8y^2
Combine them with the first two terms and it'll be like below.
= - x^2 + 9xy - x^2 - 6xy + 8y^2
Then, rearrange and sum all like terms together.
There are 2 sets of like terms:
First set: (- x^2 and- x^2)
Second set: ( + 9xy and - 6xy)
So, it becomes...
= - x^2 - x^2 + 9xy - 6xy + 8y^2
= - 2x^2 + 3xy + 8y^2