Multiply $(a + b)$ by $(a^{2} - ab + b^{2})$.

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

Solution

$(a+b)(a^{2} - ab + b^{2}) = a^{3} - a^{2}b + ab^{2} + a^{2}b - ab^{2} + b^{3} = a^{3} + b^{3}$.

Asked in: IMO

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