SOLUTION: How do I completely factor {{{81x^4-16}}}?

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Question 9656: How do I completely factor 81x%5E4-16?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to recognise this as the difference of two squares, and this factors like:
a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29
81x%5E4+-+16+=+%289x%5E2+-+4%29%289x%5E2+%2B+4%29
Again, you have the difference of two squares, so this will factor.
%283x-2%29%283x%2B2%29%289x%5E2%2B4%29
If you really want to factor completely, the the sum of two squares can be factored: %28a%5E2+%2B+b%5E2%29+=+%28a+-+bi%29%28a+%2B+bi%29 where: +i+=+sqrt%28-1%29
The complete factorisation then is: %283x-2%29%283x%2B2%29%283x-2i%29%283x%2B2i%29
If you are not yet into complex numbers, then leave it at: %283x-2%29%283x%2B2%29%289x%5E2%2B4%29