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Mathematics

Factorise:

x6 - 1

Factorisation

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Answer

Given,

⇒ x6 - 1

⇒ (x3)2 - (1)2

By using the identity,

(a2 - b2) = (a + b)(a - b)

⇒ (x3 - 1)(x3 + 1)

⇒ [x3 - (1)3][x3 + (1)3]

⇒ (x - 1)[(x)2 + x × 1 + 12] [(x + 1)(x)2 - x × 1 + 12]

⇒ (x - 1)(x2 + x + 1)(x + 1)(x2 - x + 1)

⇒ (x - 1)(x + 1)(x2 + x + 1)(x2 - x + 1).

Hence, x6 - 1 = (x - 1)(x + 1)(x2 + x + 1)(x2 - x + 1).

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