Find $(a + b)^{2} + (a - b)^{2}$.

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

Solution

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

Asked in: IMO

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