Factorise $4 x^{2} - 12 a x - y^{2} - z^{2} - 2 y z + 9 a^{2}$

(2 x^{2} - 3 a + y + z) (2 x - 3 a^{2} - 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^{2} - 3 a - y - z^{3})

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(2 x - 3 a + y + z) (2 x - 3 a^{3} - y + z)

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Solution

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

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