SOLUTION: I need to factor X^6 + 64 using complex numbers. Please help!

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Question 17314: I need to factor X^6 + 64 using complex numbers. Please help!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You need to recognise this expression as the sum of two cubes.
x%5E6+%2B+64+=+%28x%5E2%29%5E3+%2B+4%5E3
The sum of two cubes is factored as:
A%5E3+%2B+b%5E3+=+%28A+%2B+B%29%28A%5E2+-+AB+%2B+B%5E2%29
%28x%5E2%29%5E3+%2B+4%5E3+=+%28x%5E2+%2B+4%29%28x%5E4+-+4x%5E2+%2B+16%29 Now factor the %28x%5E2+%2B+4%29 as the sum of two squares.
x%5E2+%2B+4+=+%28x+%2B+2i%29%28x+-+2i%29
Finally:
x%5E6+%2B+64+=+%28x+%2B+2i%29%28x+-+2i%29%28x%5E4+-+4x%5E2+%2B+16%29