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

x^{2} - 6 y^{2} - 2 x y

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- x^{2} + 6 y^{2} + 2 x y

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x^{2} - 6 y^{2} + 2 x y

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- x^{2} + 6 y^{2}

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Solution

The correct option is B $- x^{2} + 6 y^{2} + 2 x y$
We have to find what should be added to $2 x^{2} - 3 y^{2}$ to get $x^{2} + 3 y^{2} + 2 x y$
If we subtract $2 x^{2} - 3 y^{2}$ form $x^{2} + 3 y^{2} + 2 x y$ we will get our expression.

$⟹ (x^{2} + 3 y^{2} + 2 x y) - (2 x^{2} - 3 y^{2})$
Step 1: Open the brackets and change the sign of 2nd expression
$⟹ x^{2} + 3 y^{2} + 2 x y - 2 x^{2} + 3 y^{2}$
Step 2: Group the like terms
$⟹ (x^{2} - 2 x^{2}) + (3 y^{2} + 3 y^{2}) + 2 x y ⟹ - x^{2} + 6 y^{2} + 2 x y$

Hence, option B is correct.

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