$What should be subtracted from 2 x^{2} - 4 y^{2} + 6 x y + 10 to obtain - 2 x^{2} - 3 y^{2} + 6 x y + 10 ?$

4 x^{2} - y^{2} + 20

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4 x^{2} - y^{2} - 20

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

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

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Solution

The correct option is C $4 x^{2} - y^{2}$
Let the expression to be subtracted be $A$ .

$\Rightarrow (2 x^{2} - 4 y^{2} + 6 x y + 10) - A = - 2 x^{2} - 3 y^{2} + 6 x y + 10$

$\Rightarrow A = (2 x^{2} - 4 y^{2} + 6 x y + 10) - (- 2 x^{2} - 3 y^{2} + 6 x y + 10)$

Grouping the like terms together,
$\Rightarrow A = (2 x^{2} + 2 x^{2}) + (- 4 y^{2} + 3 y^{2}) + (6 x y - 6 x y) + (10 - 10)$

$\Rightarrow$ $A = 4 x^{2} - y^{2}$

Hence, the expression that needs to be subracted is $4 x^{2} - y^{2}$ .

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What should be subtracted from 2 x^{2} - 4 y^{2} + 6 x y + 10 to obtain - 2 x^{2} - 3 y^{2} + 6 x y + 10 ?

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