What must be added to $x y + 3 x - 2 y$ to get $7 x + 5 y$ ?

4x + 7y - xy

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4x + 7y + xy

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4x - 7y - xy

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4x - 7y + xy

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Solution

The correct option is A
4x + 7y - xy

Let the required algebraic expression be P.
$∴ P + (x y + 3 x - 2 y) = 7 x + 5 y$
$\Rightarrow P = 7 x + 5 y - (x y + 3 x - 2 y)$
$\Rightarrow P = 7 x + 5 y - x y - 3 x + 2 y$ [Opening brackets]

Group like terms together.
$\Rightarrow P = (7 x - 3 x) + (5 y + 2 y) - x y$
$\Rightarrow P = 4 x + 7 y - x y$

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