${(x - y - z)}^{2} - {(x + y + z)}^{2}$ is equal to :

4 x y + 4 y z

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- 4 x y - 4 x z

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4 x y + 4 x z

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- 4 y z

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Solution

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

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

= $- 4 x y - 4 x z$

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