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

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Solution

Given : $9 x^{2} + 16 y^{2} + 4 z^{2} - 24 x y + 16 y z - 12 x z$
According to the equation,
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
So we get,
Using the formula we can it write it as
$9 x^{2} + 16 y^{2} + 4 z^{2} - 24 x y + 16 y z - 12 x z$ $= (- 3 x)^{2} + (4 y)^{2} + (2 z)^{2} + 2 (- 3 x) (4 y) + 2 (4 y) (2 z) + 2 (2 z) (- 3 x)$
On further calculation we get,
$9 x^{2} + 16 y^{2} + 4 z^{2} - 24 x y + 16 y z - 12 x z$ $= (- 3 x + 4 y + 2 z)^{2}$
It can be written as

$9 x^{2} + 16 y^{2} + 4 z^{2} - 24 x y + 16 y z - 12 x z$ $= (- 3 x + 4 y + 2 z) (- 3 x + 4 y + 2 z)$

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Factorise the following:

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