How do you factor #(r^3 - 1)#?

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Answer 1 · 2016-07-31T16:58:17

#r^3-1=(r-1)(r^2+r+1)#

One can either use the identity #(a^3-b^3)=(a-b)(a^2+ab+b^2)#, so that

#r^3-1=r^3-1^3=(r-1)(r^2+rxx1+1^2)=(r-1)(r^2+r+1)#

We can also factorize following way

#r^3-1#

= #r^3-r^2+r^2-r+r-1#

= #r^2(r-1)+r(r-1)+1(r-1)#

= #(r-1)(r^2+r+1)#