Evaluate:
$8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3} + x^{2} y^{2} z^{2}) + 4 x^{2} y^{2} z^{2}$

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Solution

We have,
$8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3} + x^{2} y^{2} z^{2}) + 4 x^{2} y^{2} z^{2}$

$\Rightarrow 8 x^{3} y^{2} z^{2} + 8 x^{2} y^{3} z^{2} + 8 x^{2} y^{2} z^{3} + 8 x^{2} y^{2} z^{2} + 4 x^{2} y^{2} z^{2}$

$\Rightarrow 8 x^{3} y^{2} z^{2} + 8 x^{2} y^{3} z^{2} + 8 x^{2} y^{2} z^{3} + 12 x^{2} y^{2} z^{2}$

$\Rightarrow 4 (x^{2} y^{2} z^{2}) (2 x + 2 y + 2 z + 3)$

Hence, this is the answer.

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