The expansion of $(p + q + r)^{2}$ is

The expansion of $(p + q + r)^{2}$ is
  1. $p^{2} + q^{2} + r^{2} + 2pq + 2qr + 2pr$
  2. $p^{2} + q^{2} + r^{2} + pq + qr + pr$
  3. $p^{2} + q^{2} + r^{2} + 2pqr$
  4. $p^{2} + q^{2} + r^{2}$

Solution

$(p+q+r)^{2} = p^{2}+q^{2}+r^{2} + 2(pq + qr + pr)$.

Asked in: IMO

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