Mathematics
Factorise the following:
x6 - 1
Factorisation
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Answer
x6 - 1 = (x3)2 - (1)2.
We know that,
a2 - b2 = (a + b)(a - b).
∴ (x3)2 - (1)2 = (x3 - 1)(x3 + 1).
We know that,
a3 - b3 = (a - b)(a2 + ab + b2).
a3 + b3 = (a + b)(a2 - ab + b2).
∴ (x3 - 1)(x3 + 1) = (x - 1)(x2 + x + 1)(x + 1)(x2 - x + 1)
Hence, x6 - 1 = (x - 1)(x + 1)(x2 + x + 1)(x2 - x + 1).
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