Alex went for shopping with $5 x^{2} + 3 x y - y^{3}$ rupees. He bought a toy for $2 x^{2} + x y$ rupees and spent $2 x y - y^{3}$ rupees on a meal. How much money is he left with?

3 x^{2}

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7 x^{2} + 6 x y - 2 y^{3}

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7 x^{2} + 2 x y

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3 x^{2} + 4 x y - 2 y^{3}

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Solution

The correct option is A $3 x^{2}$
Total money which Alex had $= 5 x^{2} + 3 x y - y^{3}$
Money spent on buying the toy $= 2 x^{2} + x y$
Money spent on meal
$= 2 x y - y^{3}$

Total money spent
$= (2 x^{2} + x y) + (2 x y - y^{3})$
$= 2 x^{2} + 3 x y - y^{3}$

Now, money left = Total money – Money spent

Hence, money left
$= (5 x^{2} + 3 x y - y^{3}) - (2 x^{2} + 3 x y - y^{3})$
$= 5 x^{2} + 3 x y - y^{3} - 2 x^{2} - 3 x y + y^{3}$
$= 5 x^{2} - 2 x^{2} + 3 x y - 3 x y - y^{3} + y^{3}$
$= 3 x^{2}$

So, the money that is left with Alex is $3 x^{2}$ rupees.

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