Each symbol given below represents an algebraic expression.

The symbols are then represented in the expression

Find the expression which is represented by the above symbols.

10 x^{2} + 8 y^{2} + x

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10 x^{2} - 8 y^{2} + x

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10 x^{2} - 3 y - 8 y^{2} + x

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10 x^{2} + 8 y^{2} + 3 y + x

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Solution

The correct option is B $10 x^{2} - 8 y^{2} + x$
Given,

and

$∴$

$= (2 x^{2} + 3 y) + (5 x^{2} + 3 x) - (8 y^{2} - 3 x^{2} + 2 x + 3 y) = 2 x^{2} + 3 y + 5 x^{2} + 3 x - 8 y^{2} + 3 x^{2} - 2 x - 3 y$
On grouping the like terms,
$= (2 x^{2} + 5 x^{2} + 3 x^{2}) + (3 y - 3 y) + (3 x - 2 x) - 8 y^{2}$
Solving the groups,
$= 10 x^{2} - 8 y^{2} + x$

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