Expand $(x + 9)(x - 9)$.

Expand $(x + 9)(x - 9)$.
  1. $x^{2} - 81$
  2. $x^{2} + 81$
  3. $x^{2} - 18x + 81$
  4. $x^{2} - 18$

Solution

$(a+b)(a-b) = a^{2} - b^{2}$ with $a = x,\ b = 9$: $x^{2} - 81$.

Asked in: IMO

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