Expand $\left(\dfrac{1}{2}x - 3y\right)^{2}$.

Expand $\left(\dfrac{1}{2}x - 3y\right)^{2}$.
  1. $\dfrac{x^{2}}{4} - 3xy + 9y^{2}$
  2. $\dfrac{x^{2}}{4} + 3xy + 9y^{2}$
  3. $\dfrac{x^{2}}{2} - 3xy + 9y^{2}$
  4. $\dfrac{x^{2}}{4} - 6xy + 9y^{2}$

Solution

$\left(\dfrac{x}{2}\right)^{2} - 2 \cdot \dfrac{x}{2} \cdot 3y + (3y)^{2} = \dfrac{x^{2}}{4} - 3xy + 9y^{2}$.

Asked in: IMO

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