$8 (3 x - 2 y)^{2} - 6 x + 4 y - 1$

$(12 x - 4 y + 1) (6 x + 8 y - 1)$

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$(12 x - 8 y - 1) (6 x + 4 y + 1)$

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$(12 x + 8 y + 1) (6 x + 4 y - 1)$

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$(12 x - 8 y + 1) (6 x - 4 y - 1)$

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Solution

The correct option is D
$(12 x - 8 y + 1) (6 x - 4 y - 1)$

Given $8 (3 x - 2 y)^{2} - 6 x + 4 y - 1$

$8 (3 x - 2 y)^{2} - 2 (3 x - 2 y) - 1$ ( taking 2 common in the second term )
Let $3 x - 2 y = a$

$\Rightarrow 8 a^{2} - 2 a - 1$

$\Rightarrow 8 a^{2} - 4 a + 2 a - 1$ ( splitting the middle term as -4a and 2a )

$\Rightarrow 4 a (2 a - 1) + 1 (2 a - 1)$
$\Rightarrow (4 a + 1) (2 a - 1)$
Re-substituting $a = 3 x - 2 y$
$\Rightarrow (4 (3 x - 2 y) + 1) (2 (3 x - 2 y) - 1)$
$\Rightarrow (12 x - 8 y + 1) (6 x - 4 y - 1)$

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