What should be added to $5 x^{2} + 2 x y + y^{2}$ to get $3 x^{2} + 4 x y$ ?

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

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

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

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

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Solution

The correct option is A $- 2 x^{2} + 2 x y - y^{2}$
Let $A = 3 x^{2} + 4 x y$ and $B = 5 x^{2} + 2 x y + y^{2}$
Let $C$ be the required expression
Now, $A = B + C$
$=> C = A - B$
Thus, $3 x^{2} + 4 x y - (5 x^{2} + 2 x y + y^{2})$
$= 3 x^{2} + 4 x y - 5 x^{2} - 2 x y - y^{2}$
$= - 2 x^{2} + 2 x y - y^{2}$

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