Expand $(3x + 4y)^{2}$.

Expand $(3x + 4y)^{2}$.
  1. $9x^{2} + 24xy + 16y^{2}$
  2. $9x^{2} + 12xy + 16y^{2}$
  3. $9x^{2} + 24xy - 16y^{2}$
  4. $3x^{2} + 24xy + 4y^{2}$

Solution

$(3x)^{2} + 2(3x)(4y) + (4y)^{2} = 9x^{2} + 24xy + 16y^{2}$.

Asked in: IMO

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