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

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Solution

We have $4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z .$

$= {(2 x)}^{2} + {(3 y)}^{2} + {(- 4 z)}^{2} + 2 (2 x) (3 y) - 2 (3 y) (4 z) - 2 (2 x) (4 z)$

$= {(2 x)}^{2} + {(3 y)}^{2} + {(- 4 z)}^{2} + 2 (2 x) (3 y) + 2 (3 y) (- 4 z) + 2 (2 x) (- 4 z)$

Using identity, ${(x + y + z)}^{2}$ = $x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 z x$
$= {(2 x + 3 y - 4 z)}^{2}$

$= (2 x + 3 y - 4 z) (2 x + 3 y - 4 z)$

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Similar questions

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)

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

2 x^{2} + y^{z} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 x z

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

P (x)

x = 1, y = 1, z = 1.

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

(i) 4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z (i i) 2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 x z

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