Factorise $8x^{3} - 27$.

Factorise $8x^{3} - 27$.
  1. $(2x - 3)(4x^{2} + 6x + 9)$
  2. $(2x + 3)(4x^{2} - 6x + 9)$
  3. $(2x - 3)(4x^{2} - 6x + 9)$
  4. $(2x - 3)^{3}$

Solution

$8x^{3}-27 = (2x)^{3}-3^{3} = (2x-3)\big[(2x)^{2}+(2x)(3)+3^{2}\big] = (2x-3)(4x^{2}+6x+9)$.

Asked in: IMO

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