SOLUTION: Factor: 216x^3-1

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Question 813290: Factor:
216x^3-1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
216x%5E3-1
The GCF of this is 1 (which we rarely bother factoring out). Among the factoring patterns there are only two which have two terms with a subtraction between them:
  • a%5E2-b%5E2=%28a%2Bb%29%28a-b%29
  • a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
So if our expression is a difference of squares or a difference of cubes we can use the appropriate pattern to factor it.

With the x%5E3 this is not a difference of squares. Is it a difference of cubes? Well, the 1 is the same as 1 cubed so that's good. But what about the 216? With a little investigation of perfect cubes we should find that 216 is 6 cubed. So we can rewrite the expression as a difference of cubes:
%286x%29%5E3-%281%29%5E3
Using '6x' for the 'a' and '1' for the 'b', the pattern gives us:

Neither factor will factor further so we are finished.