Expand $(2a + 3b)^{2}$.

Expand $(2a + 3b)^{2}$.
  1. $4a^{2} + 12ab + 9b^{2}$
  2. $4a^{2} + 6ab + 9b^{2}$
  3. $2a^{2} + 12ab + 3b^{2}$
  4. $4a^{2} + 9b^{2}$

Solution

$(2a)^{2} + 2(2a)(3b) + (3b)^{2} = 4a^{2} + 12ab + 9b^{2}$.

Asked in: IMO

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