SOLUTION: factor b^6-1

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Question 168970: factor b^6-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

b%5E6-1 Start with the given expression.


%28b%5E2%29%5E3-%281%29%5E3 Rewrite b%5E6 as %28b%5E2%29%5E3. Rewrite 1 as %281%29%5E3.


%28b%5E2-1%29%28%28b%5E2%29%5E2%2B%28b%5E2%29%281%29%2B%281%29%5E2%29 Now factor by using the difference of cubes formula. Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%28b%5E2-1%29%28b%5E4%2Bb%5E2%2B1%29 Multiply


%28b%2B1%29%28b-1%29%28b%5E4%2Bb%5E2%2B1%29 Factor b%5E2-1 to get %28b%2B1%29%28b-1%29 (by use of the difference of squares)


%28b%2B1%29%28b-1%29%28b%5E2%2Bb%2B1%29%28b%5E2-b%2B1%29 Factor b%5E4%2Bb%5E2%2B1 to get %28b%5E2%2Bb%2B1%29%28b%5E2-b%2B1%29

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Answer:

So b%5E6-1 completely factors to %28b%2B1%29%28b-1%29%28b%5E2%2Bb%2B1%29%28b%5E2-b%2B1%29.

In other words, b%5E6-1=%28b%2B1%29%28b-1%29%28b%5E2%2Bb%2B1%29%28b%5E2-b%2B1%29