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

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Solution

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

$\Rightarrow (2 x)^{2} + (3 y)^{2} + (4 z)^{2} + 2 x (2 x) (3 y) + 2 \times 3 y \times 4 z + 2 \times 2 x \times 4 z$

we know that
$(a + b - c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b - 2 b c - 2 c a$

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

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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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