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What is the completely factored form of the expression 27y cubed minus1?
Wiki User
∙ 13y ago
Fortunately, one of the three roots of 27y3 - 1 is really obvious, y = 1/3. Therefore we can pull (y - 1/3) out of the expression giving us:
(y - 1/3)(27y2 + 9y +3).
Using the quadratic formula on the second multiplicative expression gives:
[-9 ± √(-243)]/54 = (-9 ± 9i√3)/54.
So the complete, factored form of 27y3 - 1 is:
(y - 1/3)[y - (9 + 9i√3)/54][y - (9 - 9i√3)/54].
Wiki User
∙ 13y ago
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