Factorize the equation $4 x y - x^{2} - 4 y^{2} + z^{2}$

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

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

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

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none of the above

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Solution

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

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