State True or False.
$27 x^{3} + y^{3} + z^{3} - 9 x y z$ $= (3 x + y + z) [(9 x^{2} + y^{2} + z^{2} - 3 x y - y z - 3 z x)]$

True

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False

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Solution

The correct option is A True
We have, $27 x^{3} + y^{3} + z^{3} - 9 x y z = (3 x)^{3} + (y)^{3} + (z)^{3} - 3 (3 x) (y) (z)$
$= (3 x + y + z) [(3 x)^{2} + y^{2} + z^{2} - (3 x) y - y z - z (3 x)]$
$= (3 x + y + z) [(9 x^{2} + y^{2} + z^{2} - 3 x y - y z - 3 z x)]$

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Similar questions

27 x^{3} + y^{3} + z^{3} - 9 x y z

x^{3} + y^{3} + z^{3} - 3 x y z = \frac{1}{2} (x + y + z) [(x - y)^{2} + (y - z)^{2} + (z - x)^{2}]

x^{3} + y^{3} + z^{3} - 3 x y z \geq (x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x)

3 x + y + z = 0

27 x^{3} + y^{3} + z^{3} = 9 x y z

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