Question

How do you simplify x^2+y^2?

Answer 1

The other responder is correct. There is nothing more to be done.

You may think this is a trivial response, but it is a good one. It teaches you not to destroy plus signs by combining unlike terms. You should treat this as a "can you combine apples and oranges" problem. 

In other words, is there any similarity between apples and oranges other than both are fruits? You should answer no there is no similarity.

Same with xs and ys. There is no similarity. until you are told there is.

Answer<<<<< nothing can be done.

Answer 2

Nothing further can be done, its x^2+y^2