(a²-3ab+b²)+(-a²+3ab+b²)

To simplify the expression (a²-3ab+b²)+(-a²+3ab+b²), we can combine like terms.

Starting with the first set of terms, (a²-3ab+b²):

There are no like terms to combine within this set.

Moving on to the second set of terms, (-a²+3ab+b²):

We have a² and -a², which are like terms with opposite signs. When we add these together, they cancel each other out, resulting in 0.

Now, let's combine the remaining like terms, 3ab and -3ab:

3ab + (-3ab) = 0

Finally, combining both sets of terms:

(a²-3ab+b²)+(-a²+3ab+b²) = (0) + (0) = 0