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Algebraic Expression

What must be ...

Question

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

A

3 x + 2 x y - 8 y

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B

- 4 x - x y + 2 y

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C

4 x - x y + 7 y

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D

2 x y + 2 y

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Solution

The correct option is C $4 x - x y + 7 y$
Let the required algebraic expression be P.
$∴ P + (x y + 3 x - 2 y) = 7 x + 5 y$
$\Rightarrow P = 7 x + 5 y - (x y + 3 x - 2 y)$

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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