Subtract the second expression from the first:
$5 x^{2} + 4 y^{2} - 6 y + 8$ and $x^{2} - 5 y^{2} + 2 x y + 3 y - 10$

4 x y^{2} + 9 x y^{2} + 9 y - 2 y + 12

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4 x^{y} + 9 y^{3} + 9 y + 2 x y + 18

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4 x^{2} + 9 y^{2} - 9 y - 2 x y + 18

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x^{2} + 9 y^{2} - 9 y - 2 x y + 12

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Solution

The correct option is B $4 x^{2} + 9 y^{2} - 9 y - 2 x y + 18$
$5 x^{2} + 4 y^{2} - 6 y + 8$ ; $x^{2} - 5 y^{2} + 2 x y + 3 y - 10$
$= 5 x^{2} + 4 y^{2} - 6 y + 8 - (x^{2} - 5 y^{2} + 2 x y + 3 y - 10)$
$= 5 x^{2} + 4 y^{2} - 6 y + 8 - x^{2} + 5 y^{2} - 2 x y - 3 y + 10$
$= 4 x^{2} + 9 y^{2} - 9 y - 2 x y + 18$

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