Factorise $a^{3} - 3a^{2}b + 3ab^{2} - b^{3}$.

Factorise $a^{3} - 3a^{2}b + 3ab^{2} - b^{3}$.
  1. $(a - b)^{3}$
  2. $(a + b)^{3}$
  3. $(a - b)(a^{2} + ab + b^{2})$
  4. $(a - b)(a^{2} - ab + b^{2})$

Solution

Recognise the expansion of $(a-b)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3}$.

Asked in: IMO

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