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

$r^3-1$

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

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

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

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