Factorise $27x^{3} + 64y^{3}$.

Factorise $27x^{3} + 64y^{3}$.
  1. $(3x + 4y)(9x^{2} - 12xy + 16y^{2})$
  2. $(3x - 4y)(9x^{2} + 12xy + 16y^{2})$
  3. $(3x + 4y)(9x^{2} + 12xy + 16y^{2})$
  4. $(3x + 4y)^{3}$

Solution

$27x^{3}+64y^{3} = (3x)^{3}+(4y)^{3} = (3x+4y)\big[(3x)^{2}-(3x)(4y)+(4y)^{2}\big] = (3x+4y)(9x^{2}-12xy+16y^{2})$.

Asked in: IMO

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