### Brain Teasers

# x^2 - y^2

Lester is very intent on finding a formula to calculate the difference between two squares but doesn't have any squared terms in it.

Eg: If x and y are two numbers with y>x then he wants to find a formula to calculate (y^2)-(x^2) which does not contain any x^2 or y^2 terms in it.

He finds that there are two cases:

a) when x and y are consecutive.

b) when x and y are not consecutive.

Can you help him find the formula?

Eg: If x and y are two numbers with y>x then he wants to find a formula to calculate (y^2)-(x^2) which does not contain any x^2 or y^2 terms in it.

He finds that there are two cases:

a) when x and y are consecutive.

b) when x and y are not consecutive.

Can you help him find the formula?

### Hint

Take some consecutive and nonconsecutive examples and try for yourself.### Answer

a) when x and y are consecutive, the difference between their squares is given by :difference = x + y.

b) when x and y are not consecutive, the difference between their squares is given by :

difference = x + y + 2 * (sum of numbers between x and y)

You should note that part (a) is just a simplified version of (b), in which there are no numbers between x and y.

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