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Expression Formation

What will be ...

Question

What will be the expression for the sum of the squares of the numbers $x$ and $y$ , which is subtracted from the square of their difference?

A

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

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B

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

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C

- 2 x y

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D

2 x^{2} + 2 y^{2} + 2 x y

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Solution

The correct option is C $- 2 x y$
The sum of square of the numbers $x$ and $y$
$= x^{2}$ + $y^{2}$ ,

The square of their difference
$= (x - y)^{2}$ .

Hence, the final expression will be
$= (x - y)^{2} - (x^{2} + y^{2})$
$= x^{2} + y^{2} - 2 x y - x^{2} - y^{2}$
$= - 2 x y$

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