Question 8211: How do I simplify this problem?
a^2 - 2ab + b^2 / a + b
Answer by glabow(165)   (Show Source):
You can put this solution on YOUR website! 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.
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