Simplify: $(x - 3 y - 5 z) (x^{2} + 9 y^{2} + 25 z^{2} + 3 x y - 15 y z + 5 z x)$

x^{3} - 27 y^{3} - 125 z^{3} - 45 x y z

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x^{3} + 27 y^{3} - 125 z^{3} - 45 x y z

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x^{3} - 27 y^{3} + 125 z^{3} - 45 x y z

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Solution

The correct option is A $x^{3} - 27 y^{3} - 125 z^{3} - 45 x y z$
We have,
$(x - 3 y - 5 z) (x^{2} + 9 y^{2} + 25 z^{2} + 3 x y - 15 y z + 5 z x)$

$\Rightarrow (x^{3} + 9 x y^{2} + 25 x z^{2} + 3 x^{2} y - 15 x y z$
$+ 5 z x^{2} - 3 x^{2} y - 27 y^{3} - 75 y z^{2} - 9 x y^{2} +$
$45 y^{2} z - 15 x z y - 5 x^{2} z - 45 y^{2} z - 125 z^{3} - 15 x y z + 75 y z^{2} - 25 x z^{2})$

$\Rightarrow x^{3} + x y^{2} (9 - 9) + x z^{2} (25 - 25) + x^{2} y (3 - 3) - 15 x y z - 15 x z y - 15 x y z$
$+ z x^{2} (5 - 5) - 27 y^{3} + y z^{2} (- 75 + 75) - 125 z^{3} + y^{2} z (45 - 45)$

$\Rightarrow x^{3} - 27 y^{3} - 125 z^{3} - 45 x y z$

Hence, this is the answer.

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