Subtract $x + 4 x y - y^{2}$ from $3 x^{2} + 8 x y - 6 y^{2} + 2 y$

3 x^{2} - x y^{3} + 2 y - x

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3 x^{2} + 4 x y - 5 y^{2} + x y

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

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3 x^{2} + 4 x y - 5 y^{2} + 2 y - x

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Solution

The correct option is D $3 x^{2} + 4 x y - 5 y^{2} + 2 y - x$
To subtract $x + 4 x y - y^{2}$ from $3 x^{2} + 8 x y - 6 y^{2} + 2 y$ , we change the sign of every term in the expression $x + 4 x y - y^{2}$ and then add it to $3 x^{2} + 8 x y - 6 y^{2} + 2 y$ , following the rules of addition of two algebraic expressions.
What we get is,
$3 x^{2} + 8 x y - 6 y^{2} + 2 y$
$- 4 x y + y^{2}$ $- x$
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$3 x^{2} + 4 x y - 5 y^{2} + 2 y - x$

Hence the difference between the two expressions is $3 x^{2} + 4 x y - 5 y^{2} + 2 y - x$

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