The sum of two expressions is $9 x^{2} + 4 x y - 7 y^{2}$ . If one of them is $6 x^{2} + 5 x y - 12 y^{2}$ , find the other expression.

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

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

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

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

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Solution

The correct option is D $3 x^{2} - x y + 5 y^{2}$
Let the other expression be $E$ .

We are given that the sum of the expressions $6 x^{2} + 5 x y - 12 y^{2}$ and $E$ is $9 x^{2} + 4 x y - 7 y^{2}$ .

$\Rightarrow E + (6 x^{2} + 5 x y - 12 y^{2}) = (9 x^{2} + 4 x y - 7 y^{2})$

subtracting $(6 x^{2} + 5 x y - 12 y^{2})$ from both sides

$\Rightarrow E = (9 x^{2} + 4 x y - 7 y^{2}) - (6 x^{2} + 5 x y - 12 y^{2})$

This can be evaluated using column method as:

$\Rightarrow E = 3 x^{2} - x y + 5 y^{2}$

Thus, the other expression is $3 x^{2} - x y + 5 y^{2}$ .

Therefore, option (d.) is the correct answer.

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