Factorise $9a^{2} + 24ab + 16b^{2}$.

Factorise $9a^{2} + 24ab + 16b^{2}$.
  1. $(3a + 4b)^{2}$
  2. $(3a - 4b)^{2}$
  3. $(9a + 16b)(a + b)$
  4. $(3a + 4b)(3a - 4b)$

Solution

$9a^{2}+24ab+16b^{2} = (3a)^{2} + 2 \cdot 3a \cdot 4b + (4b)^{2} = (3a+4b)^{2}$.

Asked in: IMO

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