Divide $2 x^{3} y - 6 x^{2} y^{3} + 6 x^{2} y^{2}$ by $2 x^{2} y$ .

$x - 3 y^{2} + 2 y$

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$x - 2 y^{2} + 3 y$

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$x - 3 y^{2} + 3 y$

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$x - 3 y^{2} - 3 y$

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Solution

The correct option is C
$x - 3 y^{2} + 3 y$

Given : Divide $2 x^{3} y - 6 x^{2} y^{3} + 6 x^{2} y^{2}$ by $2 x^{2} y$ .

Dividing each term separately we get,

$\frac{2 x^{3} y}{2 x^{2} y}$ - $\frac{6 x^{2} y^{3}}{2 x^{2} y}$ + $\frac{6 x^{2} y^{2}}{2 x^{2} y}$

= $x - 3 y^{2} + 3 y$

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