How do you factor #r^3 - 1#?
1 Answer
Dec 20, 2015
Use the difference of cubes identity to find:
#r^3-1 = (r-1)(r^2+r+1)#
Explanation:
The difference of cubes identity can be written:
#a^3-b^3=(a-b)(a^2+ab+b^2)#
Use this with
#r^3-1#
#=r^3-1^3#
#=(r-1)(r^2+(r)(1)+1^2)#
#=(r-1)(r^2+r+1)#
If you allow Complex coefficients then this can be factored a little further:
#=(r-1)(r-omega)(r-omega^2)#
where