Simplify the following:
$(x - 2 y) (y - 3 x) + (x + y) (x - 3 y) - (y - 3 x) (4 x - 5 y)$

10 x^{2} - 14 x y

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10 x^{2} + 14 x y

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10 x^{2} + 4 x y

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None of these

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Solution

The correct option is C $10 x^{2} - 14 x y$
Simplify the following:
$(x - 2 y) (y - 3 x) + (x + y) (x - 3 y) - (y - 3 x) (4 x - 5 y)$
$(x - 2 y) (y - 3 x) + (x + y) (x - 3 y) - (y - 3 x) (4 x - 5 y)$
$x y - 3 x^{2} - 2 y^{2} + 6 x y + x^{2} - 3 x y + x y - 3 y^{2} - 4 x y + 5 y^{2} + 12 x^{2} - 15 x y$
$x^{2} (- 3 + 1 + 12) + x y (1 + 6 - 3 + 1 - 4 - 15) + y^{2} (- 2 - 3 + 5)$
$10 x^{2} - 14 x y$

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