The algebraic expression $4 x^{2} + 9 y^{2} + 25 z^{2} + 12 x y - 30 y z - 20 z x$ can be factorised as

(2 x + 3 y + 5 z)^{2}

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(2 x + 3 y - 5 z)^{2}

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(2 x - 3 y + 5 z)^{2}

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None of these

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Solution

The correct option is B $(2 x + 3 y - 5 z)^{2}$
Given, $4 x^{2} + 9 y^{2} + 25 z^{2} + 12 x y - 30 y z - 20 z x$
$= (2 x)^{2} + (3 y)^{2} + (5 z)^{2} + 2 (2 x) (3 y) + 2 (3 y) (- 5 z) + 2 (- 5 z) (2 x)$
$= (2 x + 3 y - 5 z)^{2}$
Option B is correct.

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Similar questions

Factorise:
$4 x^{2} + 9 y^{2} + 25 z^{2} + 12 x y + 30 y z + 20 z x$

(2 x + 3 y + 5 z)^{2}

(2 x + 3 y + 5 z)^{2}

4 x^{2} + 9 y^{2} + 25 z^{2} - 12 x y - 30 y z + 20 z x

\frac{{(2 x + 3 y + 5 z)}^{2}}{x^{2} + y^{2} + z^{2}} \leq 38

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