Question

'Sum of the squares of $x$ and $y$ is subtracted from the square of their difference' is written as

• A. $(x-y)-(x^2+y^2)$
• B. $(x-y{)}^2-(x+y)$
• C. $(x-y{)}^2-(x^2+y^2)$
• D. $(x-y{)}^2-(x^2-y^2)$

Answer 1

The correct option is C $(x-y{)}^2-(x^2+y^2)$

Squares of $x$ and $y$ are written as $x^2$ and $y^2$ respectively.
The word 'sum' refers to addition.
So, sum of squares of $x$ and $y$
$=x^2+y^2$
The word 'difference' refers to the operation subtraction.
So, difference of $x$ and $y$ = $x-y$
Then, square of the difference $=(x-y{)}^2$
It is given that 'Sum of the squares of $x$ and $y$ is subtracted from the square of their difference'.
Hence, the final expression will be
$=(x-y{)}^2-(x^2+y^2)$