Factorise $x y (z^{2} + 1) + z (x^{2} + y^{2})$ .

(x y + z) (y z + x)

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(z x + y) (x y + z)

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(y z + x) (z x + y)

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

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Solution

The correct option is B $(y z + x) (z x + y)$
Given : $x y (z^{2} + 1) + z (x^{2} + y^{2}) .$

Factorizing the above :

$\Rightarrow x y z^{2} + x y + z x^{2} + z y^{2}$

$\Rightarrow x y z^{2} + z x^{2} + x y + z y^{2}$

$\Rightarrow x z (y z + x) + y (y z + x)$

$\Rightarrow (x z + y) (y z + x)$

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