Expand the following $(x - 2 y - 4 z)^{2}$

x^{2} + 4 y^{2} + 16 z^{2} - 4 x y + 16 y z - 8 z x

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x^{2} - 4 y^{2} + 16 z^{2} - 4 x y + 16 y z - 8 z x

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x^{2} + 4 y^{2} - 16 z^{2} - 4 x y + 16 y z - 8 z x

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None of these

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Solution

The correct option is C $x^{2} + 4 y^{2} + 16 z^{2} - 4 x y + 16 y z - 8 z x$
$(x - 2 y - 4 z)^{2}$
$= x^{2} + 4 y^{2} + 16 z^{2} - 4 x y + 16 y z - 8 z x$
$= (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$

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Factorise the following:

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9 x^{2} + 4 y^{2} + 16 z^{2} + 12 x y - 16 y z - 24 x z

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