SOLUTION: Please help me to factor x^6-(1/729)

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: Please help me to factor x^6-(1/729)      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 62191: Please help me to factor x^6-(1/729)
Answer by Earlsdon(5032) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
x%5E6-%281%2F729%29 Do you recognise this as the difference of two cubes?
%28x%5E2%29%5E3+-+%281%2F9%29%5E3
The difference of two cubes can be factored:
A%5E3+-+B%5E3+=+%28A-B%29%28A%5E2%2BAB%2BB%5E2%29
In this problem, A = x^2 and B = 1/9
x%5E6-%281%2F729%29+=+%28x%5E2-%281%2F9%29%29%28x%5E4%2Bx%5E2%2F9%2B1%2F81%29 The first parentheses on the right can be factored.
x%5E6-%281%2F729%29+=+%28x%2B1%2F3%29%28x-1%2F3%29%28x%5E4%2Bx%5E2%2F9%2B1%2F81%29