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

(4 x + 3 y + 2 z) (4 x + 3 y + 2 z)

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(x + 3 y + 2 z) (4 x + 3 y + 2 z)

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

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

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Solution

The correct option is A $(4 x + 3 y + 2 z) (4 x + 3 y + 2 z)$
$16 x^{2} + 9 y^{2} + 4 z^{2} + 24 x y + 12 y z + 16 z x$
$= (4 x)^{2} + (3 y)^{2} + (2 z)^{2} + 2 \times 4 x \times 3 y + 2 \times 3 y \times 2 z + 2 \times 2 z \times 4 x$
Using, $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$= (4 x + 3 y + 2 z)^{2}$
$= (4 x + 3 y + 2 z) (4 x + 3 y + 2 z)$

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