# Product of a Sum and a Difference

How to solve the product of a sum and a difference problems: formula, examples, and their solutions.

## Formula

By using the FOIL method,

(*a* + *b*)(*a* - *b*) = *a*^{2} - *b*^{2}.

## Example 1

Put *x* and 2 into the formula.

## Example 2

Put 2*u* and 3*v* into the formula.

## Example 3

Instead of solving 103⋅97,

change this into (100 + 3)(100 - 3).

Then, by using the formula,

(100 + 3)(100 - 3) = 100^{2} - 3^{2}.

As you can see, by using the formula,

you can easily solve this product.

## Example 4

(*d* + 1)(*d* - 1) = *d*^{2} - 1^{2}.

Use the formula once again:

(*d*^{2} + 1)(*d*^{2} - 1) = (*d*^{2})^{2} - 1^{2}.