State True or False.
$4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z$ $= (2 x + 3 y - 4 z) (2 x + 3 y - 4 z)$

True

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False

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Solution

The correct option is A True
$4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z = (2 x)^{2} + (3 y)^{2} + (- 4 z)^{2} + 2 (2 x) (3 y) + 2 (3 y) (- 4 z) + 2 (- 4 z) (2 x)$
$= {2 x + 3 y + (- 4 z)}^{2} = (2 x + 3 y - 4 z)^{2}$
$= (2 x + 3 y - 4 z) (2 x + 3 y - 4 z)$

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