Evaluate: $(- x + 2 y - 3 z)^{2}$

x^{2} + 4 y^{2} - 9 z^{2} - 4 x y - 12 y z + 6 x z

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x^{2} + 4 y^{2} + 9 z^{2} - 4 x y + 12 y z + 6 x z

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + 4 y^{2} + 9 z^{2} - 4 x y - 12 y z - 6 x z

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x^{2} + 4 y^{2} + 9 z^{2} - 4 x y - 12 y z + 6 x z

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Solution

The correct option is D $x^{2} + 4 y^{2} + 9 z^{2} - 4 x y - 12 y z + 6 x z$
$(- x + 2 y - 3 z)^{2}$
Using $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$
$= (x)^{2} + (2 y)^{2} + (3 z)^{2} + 2 (- x) (2 y) + 2 (2 y) (- 3 z) + 2 (- x) (- 3 z)$
$= x^{2} + 4 y^{2} + 9 z^{2} - 4 x y - 12 y z + 6 x z$

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