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Division of a Polynomial by a Monomial

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Question

Simplify :-
$\frac{8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3})}{4 x^{2} y^{2} z^{2}}$

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Solution

$\frac{8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3})}{4 x^{2} y^{2} z^{2}}$

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

$= \frac{8 x^{2} y^{2} z^{2} (x + y + z)}{4 x^{2} y^{2} z^{2}}$

$= 2 (x + y + z)$ .

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