Simplify the algebraic expression:
$(x + 2 y) (y - 3 x) + (x + 4 y) (4 x - 3 y) - (y + 3 x) (6 x - 5 y)$ .

- 17 x^{2} + 17 x y - 5 y^{2}

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11 x^{2} - 17 x y + 5 y^{2}

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- 9 x^{2} + 15 x y - 7 y^{2}

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9 x^{2} - 15 x y + 7 y^{2}

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Solution

The correct option is A $- 17 x^{2} + 17 x y - 5 y^{2}$
Given: $(x + 2 y) (y - 3 x) + (x + 4 y) (4 x - 3 y) - (y + 3 x) (6 x - 5 y)$ .

$= {x (y - 3 x) + 2 y (y - 3 x)} + {x (4 x - 3 y) + 4 y (4 x - 3 y)} - {y (6 x - 5 y) + 3 x (6 x - 5 y)}$
$= (x y - 3 x^{2} + 2 y^{2} - 6 x y + 4 x^{2} - 3 x y + 16 x y - 12 y^{2} - 6 x y + 5 y^{2} - 18 x^{2} + 15 x y)$

Adding the like terms, we get
$\Rightarrow$ $- 17 x^{2} + 17 x y - 5 y^{2}$

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