Factorize the following expressions
$25 x^{2} + 4 y^{2} + 9 z^{2} - 20 x y + 12 y z - 30 z x$

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

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

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

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None of these

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Solution

The correct option is B $(5 x - 2 y - 3 z)^{2}$
$(5 x)^{2} + (2 y)^{2} + (3 z)^{2} - 2 (5 x) (2 y) + 2 (2 y) (3 z) - 2 (3 z) (5 x)$

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

Only $x$ is negative.

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

Or $= (5 x - 2 y - 3 z)^{2}$

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