Product of a Sum and a Difference
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 .
Now use the FOIL method to multiply the two binomials.
Notice that the middle terms are opposite and add to a zero pair.
In other words, the product of and is the square of minus the square of .
Find the product.
By the Product of a Sum and a Difference, .
Here, and .