Factorize the following algebraic expression:

$9 a^{2} - 24 a b + 16 b^{2}$

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Solution

Given: $9 a^{2} - 24 a b + 16 b^{2}$

$= (3 a)^{2} - 2 (3 a) (4 b) + (4 b)^{2}$

Using the formula, $(x - y)^{2} = x^{2} - 2 x y + y^{2}$

$= (3 a - 4 b)^{2}$

$= (3 a - 4 b) (3 a - 4 b)$

$∴ 9 a^{2} - 24 b + 16 b^{2} = (3 a - 4 b) (3 a - 4 b)$

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