Factorise :

${(x^{2} + y^{2} - z^{2})}^{2} - 4 x^{2} y^{2}$

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

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

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

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

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Solution

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

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