SOLUTION: Is this correct? A^3-1 a-1 I had: (a-1)(a-1)(a-1) a-1 = (a-1)2 Is this right? Thanks!

Algebra ->  Equations -> SOLUTION: Is this correct? A^3-1 a-1 I had: (a-1)(a-1)(a-1) a-1 = (a-1)2 Is this right? Thanks!      Log On


   

Question 607499: Is this correct?
A^3-1
a-1
I had:
(a-1)(a-1)(a-1)
a-1
= (a-1)2
Is this right?
Thanks!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Apply the special factoring case of "difference of cubes":
a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
.
Looking at the numerator:
a%5E3-1
a%5E3-1%5E3
%28a-1%29%28a%5E2%2Ba%281%29%2B1%5E2%29
%28a-1%29%28a%5E2%2Ba%2B1%29
.
so, now we can rewrite:
%28a%5E3-1%29%2F%28a-1%29+
as:
%28%28a-1%29%28a%5E2%2Ba%2B1%29%29%2F%28a-1%29+
canceling like-terms:
a%5E2%2Ba%2B1