(6x^2-xy+y^2)+(-x^2-9xy+6y^2)

just collect like powers

6x^2 - x^2 - xy - 9xy + y^2 + 6y^2
5x^2 - 10xy + 7y^2

To add these two expressions:

(6x^2 - xy + y^2) + (-x^2 - 9xy + 6y^2)

We need to combine like terms. Like terms have the same variables and the same exponents.

Let's start by combining the x^2 terms:

6x^2 + (-x^2) = 5x^2

Next, let's combine the xy terms:

-xy + (-9xy) = -10xy

Now, let's combine the y^2 terms:

y^2 + 6y^2 = 7y^2

Putting it all together:

(6x^2 - xy + y^2) + (-x^2 - 9xy + 6y^2) = 5x^2 - 10xy + 7y^2

So, the final expression is 5x^2 - 10xy + 7y^2.