Subtract $8 x y^{2} + 3 x^{2} y + 5 x - 9 y + 7$ from $7 x + y - 5 x^{2} y - 13 x y^{2} + 11.$

- 6 x - 8 y + 4 x^{2} y + 19 x y^{2} - 4

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- 2 x - 10 y + 8 x^{2} y + 21 x y^{2} - 4

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7 x + 3 y - 9 x^{2} y - 21 x y^{2} + 4

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2 x + 10 y - 8 x^{2} y - 21 x y^{2} + 4

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Solution

The correct option is D $2 x + 10 y - 8 x^{2} y - 21 x y^{2} + 4$
We have to find:
$(7 x + y - 5 x^{2} y - 13 x y^{2} + 11) - (8 x y^{2} + 3 x^{2} y + 5 x - 9 y + 7)$

Let's rearrange the terms and place the like terms together.

$= (7 x + y - 5 x^{2} y - 13 x y^{2} + 11 - 8 x y^{2} - 3 x^{2} y - 5 x + 9 y - 7)$

$= (- 5 x^{2} y - 3 x^{2} y - 13 x y^{2} - 8 x y^{2} + 7 x - 5 x + y + 9 y + 11 - 7)$

$= - 8 x^{2} y - 21 x y^{2} + 2 x + 10 y + 4$

$= 2 x + 10 y - 8 x^{2} y - 21 x y^{2} + 4$

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