The difference of two squares

You can multiply parentheses, right? And you know the two related rules we covered earlier? Good, because now you'll get another tool that will help you with parentheses. Just to remind you, this is the formula for the first rule we covered earlier. And this is the formula for the second rule we covered earlier.

But when it looks like this, these rules simply won't work anymore. Here, we have the sum times the difference. The terms of both parentheses are the same, but we have as plus sign in one pair of parentheses and a minus sign in the other. You can do this the usual way. You then get a² - ab + ab - b².

Combine similar terms. - ab cancels out ab. You get the answer a² - b². You have just calculated the difference of two squares. When multiplying two parentheses that have the same two terms, but with a plus sign in one pair of parentheses and a minus sign in the other, you use the difference of two squares. a + b times a - b = a² - b².

The difference of two squares is useful because it makes the calculations faster and simpler. But, it has another application. When you solve complicated equations, it will help to not only recognize the left side, the parentheses, but also the right side. This may help you when you need to factorize the expression.