Factorize:
$4 x^{2} - 12 a x - y^{2} - z^{2} - 2 y z + 9 a^{2}$ .

(2 x - 3 a + y + z) (2 x - a - y + z)

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(2 x - 3 a + y - z) (2 x - 3 a - y - z)

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(2 x - 3 a + y + z) (2 x - 3 a - y - z)

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(x - 3 a + y + z) (2 x - 3 a - y - z)

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Solution

The correct option is C $(2 x - 3 a + y + z) (2 x - 3 a - y - z)$
$4 x^{2} - 12 a x - y^{2} - z^{2} - 2 y z + 9 a^{2}$
$= 4 x^{2} - 12 a x + 9 a^{2} - y^{2} - z^{2} - 2 y z$
$= (2 x)^{2} - 2 (2 x) (3 a) + (3 a)^{2} - (y^{2} + 2 y z + z^{2})$ [Using $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ]
$= (2 x - 3 a)^{2} - (y + z)^{2}$ [Using $a^{2} - b^{2} = (a + b) (a - b)$ ]
$= (2 x - 3 a + y + z) (2 x - 3 a - y - z)$

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