Difference of Squares

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)


a2 - ab + ab - b2

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

(a + b)(a - b)


a2 - b2

a2 - b2 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:

a2 - b2 = (a + b)(a - b)


(a + b)(a - b) = a2 - b2

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