Factorize : $4 (2 x - 3 y)^{2} - 8 x + 12 y - 3$

(4 x - 6 y + 3) (4 x - 6 y + 1)

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(4 x - 6 y - 3) (4 x - 6 y + 1)

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(2 x - 3 y + 3) (2 x - 3 y + 1)

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Solution

The correct option is C $(4 x - 6 y - 3) (4 x - 6 y + 1)$
$4 (2 x - 3 y)^{2} - 8 x + 12 y - 3$
$= 4 (2 x - 3 y)^{2} - 4 (2 x - 3 y) - 3$
Let $(2 x - 3 y)$ be $a$
$= 4 a^{2} - 4 a - 3$
$= 4 a^{2} - 6 a + 2 a - 3$
$= 2 a (2 a - 3) + 1 (2 a - 3)$
$= (2 a - 3) (2 a + 1)$
Putting the value of $a$
$= [2 (2 x - 3 y) - 3] [2 (2 x - 3 y) + 1]$
$= (4 x - 6 y - 3) (4 x - 6 y + 1)$

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