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

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

Solution

$(a+b)^{2} - (a-b)^{2} = (a^{2}+2ab+b^{2}) - (a^{2}-2ab+b^{2}) = 4ab$.

Asked in: IMO

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