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

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

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

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= (z - x + 2 y) (z^{2} + x + 2 y^{2})

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

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Solution

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

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