The Square of a Binomial

In this lesson, we will discover a special rule that can be applied when you square a binomial.

In our last method, we studied the FOIL method for multiplying binomials. We can still apply the FOIL method when we square binomials, but we will also discover a special rule that can be applied to make this process easier. Let's take a look at Example 1.

Example 1: Investigating the Square of a Binomial

Investigating the square of a binomial

Let's take a look at a special rule that will allow us to find the product without using the FOIL method.

The square of a binomial is the sum of: the square of the first terms, twice the product of the two terms, and the square of the last term.

I know this sounds confusing, so take a look..

Squaring a binomial

If you can remember this formula, it you will be able to evaluate polynomial squares without having to use the FOIL method. It will take practice.

Now let's take a look at Example 1 and find the product using our special rule.

Example 1: Using the Special Rule

Using the special rule for squaring a binomial

Now let's take a look at another example. This time we are going to square a binomial, but this binomial will contain a subtraction sign.

Example 2: Using the Special Rule with a Negative Sign

For this example, we will not use FOIL, we will use our special rule!

Did you notice that the middle term is negative this time?

Let's quickly recap, and look at the definition for Squaring a Binomial. You might want to record this in your Algebra notes.

Squaring a Binomial

Squaring a binomial

Are you ready to practice?

Practice Problems

Squaring a binomial practice problems


Problem 1:

Squaring a binomial

Problem 2:

Finding the area of a square with polynomials

Great Job!  Now you are ready to study a new special rule which is called the "Difference of Two Squares."

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