Factorize : $(2 a + 3 b)^{2} - 16 c^{2}$

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Solution

Given expression $(2 a + 3 b)^{2} - 16 c^{2} = (2 a + 3 b)^{2} - (4 c)^{2}$
As we know that $x^{2} - y^{2} = (x + y) (x - y)$
Substitute $x = 2 a + 3 b, y = 4 c$
$\Rightarrow (2 a + 3 b)^{2} - (4 c)^{2} = (2 a + 3 b)^{2} - (4 c)^{2}$
$= (2 a + 3 b + 4 c) (2 a + 3 b - 4 c)$
Therefore, the factors of the given expression are $(2 a + 3 b + 4 c) (2 a + 3 b - 4 c)$

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