What must be subtracted from $3 x^{2} + 4 y^{2} - 5$ to get $2 x^{2} - 3 y^{2} + 5$ ?

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

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

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x^{2} + 7 y^{2} - 10

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x^{2} - 7 y^{2} - 10

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Solution

The correct option is D $x^{2} + 7 y^{2} - 10$
Subtract both expression to get the answer

$\Rightarrow (3 x^{2} + 4 y^{2} - 5) - (2 x^{2} - 3 y^{2} + 5)$

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

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

$= x^{2} + 7 y^{2} - 10$

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Question 5

What should be subtracted from $3 x^{2} - 4 y^{2} + 5 x y + 20$ to obtain $- x^{2} - y^{2} + 6 x y + 20$ ?

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

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

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