What should be added to $2 x^{2} y - 5 y^{3} x + 11 x y$ to get $10 x^{2} + 3 y^{3} x - 6 x y$

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Solution

Let z be added
$\Rightarrow 2 x^{2} y - 5 y^{3} x + 11 x y + z = 10 x^{2} + 3 y^{3} x - 6 x y$
$\Rightarrow z = 10 x^{2} + 8 y^{3} x - 17 x y - 2 x^{2} y$
$\Rightarrow z = x (10 x + 8 y^{3} - 17 y - 2 x y)$
$z = x (2 x (5 x - y) + y^{2} (8 y - 17))$ .

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