What happens when you multiply the sum of two quantities by their difference? This calculation occurs so commonly in mathematics that it's worth memorizing a formula. Write the product as (*a* + *b*)(*a* – *b*).

Now use the FOIL method to multiply the two binomials.

Notice that the middle terms are opposite and add to a zero pair.

So, (*a * + *b*)(*a * + (– *b*)) = *a*^{2 }– *b*^{2} .

In other words, the product of *a * + *b * and *a * – *b * is the square of *a * minus the square of *b *.

(*a * + *b*)(*a * – *b*) = *a*^{2} – *b*^{2}

**Example : **

Find the product.

(3*x * + 4)(3*x * – 4)

By the Product of a Sum and a Difference, (*a * + *b*)(*a * – *b*) = *a*^{2} – *b*^{2} .

Here, *a * = 3*x * and *b * = 4.

(3*x * + 4)(3*x * – 4) = (3*x*)^{2 }– (4)^{2}

Simplify.

(3*x * + 4)(3*x * – 4) = 9*x*^{2 }– 16