Multiply $\left(\dfrac{1}{2}x + 4\right)\left(\dfrac{1}{2}x - 4\right)$.

Multiply $\left(\dfrac{1}{2}x + 4\right)\left(\dfrac{1}{2}x - 4\right)$.
  1. $\dfrac{1}{4}x^{2} - 16$
  2. $\dfrac{1}{2}x^{2} - 16$
  3. $\dfrac{1}{4}x^{2} + 16$
  4. $\dfrac{1}{4}x^{2} - 8$

Solution

Apply $(a+b)(a-b) = a^{2} - b^{2}$ with $a = \dfrac{x}{2},\ b = 4$: $\dfrac{x^{2}}{4} - 16$.

Asked in: IMO

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