Question 8211
You do the division! This is called polynomial division. How many times will a+b go into a^2? a times, of course. a times a+b is a^2 + ab, so you subtract that from the polynomial to get -ab + b^2. How many times will a+b go into that? -b times. -b times a+b is -ab + b^2. You subtract that from -ab + b^2 and you get .... zero! a+b divides evenly into the original polynomial a-b times.

Of course, you might have noticed that you can factor the original polynomial as (a+b) (a-b) = a^2 -2ab + b^2. Then you would have (a+b)(a-b)/(a+b) and you would "cancel out" (a+b). Same result, of course.

It is worth learning polynomial division, however.