There is a special case example for multiplying expressions with parentheses called the difference of squares.

Consider this multiplication:

(a + b)(a - b)

If we FOIL this we get:

(a + b)(a - b)

equals

a^{2} - ab + ab - b^{2}

Notice that -ab cancels with +ab. Both of these terms, therefore, drop out, and we are left with:

(a + b)(a - b)

equals

a^{2} - b^{2}

a^{2} - b^{2} is called a difference
of squares because it is a subtraction, or difference, of two terms each of which are squared.

So, we can go back and forth each way:

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

and

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