Expand $(3p - 2q)^{2}$.

Expand $(3p - 2q)^{2}$.
  1. $9p^{2} - 12pq + 4q^{2}$
  2. $9p^{2} + 12pq + 4q^{2}$
  3. $9p^{2} - 6pq + 4q^{2}$
  4. $3p^{2} - 12pq + 2q^{2}$

Solution

$(3p)^{2} - 2(3p)(2q) + (2q)^{2} = 9p^{2} - 12pq + 4q^{2}$.

Asked in: IMO

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