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

Simplify $(a + b)^{2} + (a - b)^{2} - 2(a^{2} + b^{2})$.
  1. $0$
  2. $4ab$
  3. $2(a^{2}+b^{2})$
  4. $-4ab$

Solution

$(a+b)^{2}+(a-b)^{2} = 2(a^{2}+b^{2})$. Subtracting $2(a^{2}+b^{2})$ gives $0$.

Asked in: IMO

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