Factorise $4 x^{2} - 4 x y - z^{2} - 2 y z$ .

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

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

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

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

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Solution

The correct option is C $(2 x + z) (2 x - 2 y - z)$
$4 x^{2} - 4 x y - z^{2} - 2 y z$
$= (4 x^{2} - z^{2}) - (4 x y + 2 y z)$
$= (2 z - z) (2 x + z) - 2 y (2 x + z)$
$= (2 x + z) (2 x - z - 2 y)$

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