Squaring the binomial

Can you multiply expressions in parentheses? Good, because now you'll get two shortcuts that will make it faster and easier. Here are two parentheses to multiply. It's actually the same expression multiplied by itself. So we can write it like this as well: (x + 3)².

If you do this multiplication as usual, it looks like this. Combine similar terms to get x² + 6x + 9. If you'll do many problems where you square the parentheses, you'll soon start to realize that there's a pattern here. To see the pattern, we'll make the calculation a bit more general by using just the variables, like this. We do the same steps as before, one step at a time.

Combine similar terms. This is the first rule. A sum of two terms squared is always equal to the first term squared plus two times the product of the terms, plus the second term squared. That was the first rule. Let's look at the second rule too while we're at it.

Now, we take one parenthesis squared, where the terms are separated by a minus sign instead. If you do the multiplication, it looks like this. Multiply one term at a time. Group similar terms and simplify. And there you have a second rule.

You use it when you expand a difference of two terms squared. The only distinction from the first rule is that the middle term is negative. You have minus 2ab instead of plus 2ab. The rules for multiplying identical parentheses. Two good tools that make it easier and quicker to square parentheses.

These tools have a cousin, a difference of two squares. When you become familiar with these two, find the lesson on a difference of two squares. That's also a good tool to have.