SOLUTION: Factor completely 8x cubed - 1

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Question 110325: Factor completely
8x cubed - 1
Answer by praseenakos@yahoo.com(507) About Me  (Show Source):
You can put this solution on YOUR website!
Question:
Factor completely
8x cubed - 1
Answer:

+8x%5E3+-+1+

This can be written as,

+2%5E3+%2A+x%5E3+-+1%5E3


==> %282x%29%5E3+-+1%5E3----------------------------(1)
which is of the form +a%5E3+-+b%5E3+

Using the identity,
+a%5E3+-+b%5E3+=+%28a-b%29%28a%5E2+%2B+ab+%2B+b%5E2%29-------(2)


Comparing (1) and (2), we have, a = 2x and b = 1

So, %282x%29%5E3+-+1%5E3+=+%282x+-1%29%28%282x%29%5E2+%2B+2x+%2A+1+%2B+1%5E2%29+


==> %282x%29%5E3+-+1%5E3+=+%282x+-1%29%284x%5E2+%2B+2x+%2B+1+%29



So the factors are, (2x -1) and (4x^2 + 2x + 1)


Hope you found the explanation useful.


Regards.

Praseena.