What should be added to $6 x y + 3 y^{2} + 7 x^{2} + 2 z x$ to get $2 x^{2} + 3 x y$ ?

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

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

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

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

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Solution

The correct option is D $- 5 x^{2} - 3 x y - 3 y^{2} - 2 z x$
Let 's' be the term to be added to $(6 x y + 3 y^{2} + 7 x^{2} + 2 z x)$ to get $(2 x^{2} + 3 x y)$ .

$(6 x y + 3 y^{2} + 7 x^{2} + 2 z x) + s = (2 x^{2} + 3 x y)$
Subtract $(6 x y + 3 y^{2} + 7 x^{2} + 2 z x)$ from $(2 x^{2} + 3 x y)$

$2 x^{2} + 3 x y + 0 y^{2} + 0 z x$
$7 x^{2} + 6 x y + 3 y^{2} + 2 z x$
(-) (-) (-) (-)
_____________________
$- 5 x^{2} - 3 x y - 3 y^{2} - 2 z x$

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