Problem
ALG-B1-M02-P015 Complete Factorisation of a Sixth Power
#15
★★★☆☆ Level 3 of 5
Factor \(x^6-1\) into factors with integer coefficients.
First use difference of squares, then difference and sum of cubes.
\(x^6-1=(x^3-1)(x^3+1)\).
Also \(x^3-1=(x-1)(x^2+x+1)\), and \(x^3+1=(x+1)(x^2-x+1)\).
Thus \(x^6-1=(x-1)(x+1)(x^2+x+1)(x^2-x+1)\).
Trains a chain of standard factorisations.