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Mathematics

1 − x9 = (1 − x)(1 + x + x2) ……………

  1. 1 − x3 + x6

  2. 1 + x3 + x6

  3. 1 − x3 − x6

  4. 1 + x3 − x6

Factorisation

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Answer

Given,

⇒ 1 − x9

⇒ (1)3 − (x3)3

By using identity,

a3 - b3 = (a - b)(a2 + ab + b2)

⇒ (1 - x3)(12 + x3(1) + (x3)2)

⇒ [(1)3 - (x)3](1 + x3 + x6)

⇒ (1 - x)(12 + x(1) + x2)(1 + x3 + x6)

⇒ (1 - x)(1 + x + x2)(1 + x3 + x6).

Hence, option 2 is correct option.

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