Use $(a+b)(a-b) = a^{2} - b^{2}$ to evaluate $\dfrac{(199)^{2} - (101)^{2}}{(199 + 101)}$.

Use $(a+b)(a-b) = a^{2} - b^{2}$ to evaluate $\dfrac{(199)^{2} - (101)^{2}}{(199 + 101)}$.
  1. $98$
  2. $300$
  3. $199$
  4. $101$

Solution

$\dfrac{(199-101)(199+101)}{(199+101)} = 199 - 101 = 98$.

Asked in: IMO

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