# Writing a trinomial as the square of a binomial

Well, the first term, x2, is the square of x. So: The first term is x4, whose square root is x2. Naturally, I'm going to be thinking that the author is expecting me to notice a perfect square.

### Perfect square trinomial checker

Let's quickly recap, and look at the definition for Squaring a Binomial. This time we are going to square a binomial, but this binomial will contain a subtraction sign. Example 1: Using the Special Rule Now let's take a look at another example. So: this is not a perfect square trinomial. Let's take a look at Example 1. 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. The third term, 25, is the square of 5. But what if this is in the homework for the section in my textbook on perfect-square binomials? If you've got a match ignoring the sign , then you've got a perfect-square trinomial. This means that I'll have a "plus" sign between the x and the 5. If I use the regular methods for factoring quadratic-type polynomials , I can factor this just fine. If you can remember this formula, it you will be able to evaluate polynomial squares without having to use the FOIL method. Looking at the original quadratic they gave me, I see that the middle term is 10x, which is what I needed. Can I factor any more here?

So: this is not a perfect square trinomial. This time we are going to square a binomial, but this binomial will contain a subtraction sign.

## Perfect square trinomial formula

Squaring a Binomial Are you ready to practice? But what if this is in the homework for the section in my textbook on perfect-square binomials? The third term is 1, whose square root is just 1. 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. Example 1: 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. Well, the first term, x2, is the square of x. Affiliate I know that the first term in the original binomial will be the first square root I found, which was x. Clicking on "Tap to view steps" on the widget's answer screen will take you to the Mathway site for a paid upgrade. Try the entered exercise, or type in your own exercise.

Let's quickly recap, and look at the definition for Squaring a Binomial. The instructions say to "factor fully". Affiliate I know that the first term in the original binomial will be the first square root I found, which was x.

That's often a clue that there may be some more factoring that I could, after the usual bit is completed.

## How to make a perfect square trinomial

Clicking on "Tap to view steps" on the widget's answer screen will take you to the Mathway site for a paid upgrade. I know this sounds confusing, so take a look.. The trick to seeing this pattern is really quite simple: If the first and third terms are squares, figure out what they're squares of. Or skip the widget and continue with the lesson. But what if this is in the homework for the section in my textbook on perfect-square binomials? Try the entered exercise, or type in your own exercise. Multiplying this expression by 2, I get 10x. Did you notice that the middle term is negative this time? Content Continues Below MathHelp.

The first term, 16x2, is the square of 4x, and the last term, 36, is the square of 6. The first term, 4x2, is the square of 2x, and the last term, 36, is the square of 6 or, in this case, —6, if this is a perfect square.

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. Can I factor any more here? Let's take a look at Example 1. This is what I'm needing to match, in order for the quadratic to fit the pattern of a perfect-square trinomial.

### Perfect square trinomial calculator

Yes, I can. Can I factor any more here? With the "minus" on the middle term of what they gave me, the original squared-binomial form looks like: x2 — 1 2 Hmm Did you notice that the middle term is negative this time? Then click the button to compare your answer to Mathway's. Squaring a Binomial Are you ready to practice? I know this sounds confusing, so take a look..

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