factoring 256x^8 - 1 completely

jennal

New member
Joined
Sep 5, 2006
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3
Hi I am having difficulty with a math problem I would appreciate any help.

Factor completely:

256x^8 - 1
 
Don't know if this is right or not, but I randomly get:

\(\displaystyle 256x^8 - 1\)

\(\displaystyle =16^2(x^8)-1\)

\(\displaystyle =(16x^4)^2-1^2\)

\(\displaystyle y^2-x^2=(y-x)(y+x)\)

\(\displaystyle =(16x^4+1)(16x^4-1)\)
 
The (16x^4-1) factors to (4x^2+1)(4x^2-1)

Then the (4x^2-1) factors to (2x+1)(2x-1)
 
Thank you so much for the help. We were going in the right direction just got stumped.
 
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