SOLUTION: Factor completely: 27-8u^3 Can you please show me how to work this problem? Thank you!

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Question 328292: Factor completely:
27-8u^3
Can you please show me how to work this problem? Thank you!
Found 2 solutions by Earlsdon, mananth:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
27-8u%5E3 Rewrite this as:
-%288u%5E3%2B27%29 Notice that this is the sum of two cubes:
-%28%282u%29%5E3%2B%283%29%5E3%29 The sum of two cubes can be factored thus:
A%5E3%2BB%5E3+=++%28A%2BB%29%28A%5E2-AB%2BB%5E2%29 where A+=+2u and B+=+3 so...
-%288u%5E3%2B27%29+=+highlight%28-%282u%2B3%29%284u%5E2-6u%2B9%29%29

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
27-8u^3
(3)^3-(2u)^3
This is difference of cubes.
the general formula is a%5E3-b%5E3=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
a=3 & b= 2u
So our solution will be %283-2u%29%283%5E2%2B3%2A2u%2B%282u%29%5E2%29
%283-2u%29%289%2B6u%2B4u%5E2%29