How to Square a Trinomial

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  • 0:03 Trinomial Expressions
  • 0:17 Squaring a Trinomial
  • 2:34 Origins of the Formula
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

Trinomials are polynomials with three terms. In this lesson, we'll see how to square a trinomial using a formula and learn how the formula is derived - which gives us another way to square a trinomial!

Trinomial Expressions

In mathematics, a trinomial is an algebraic expression that has three terms and takes on the form a + b + c. The terms a, b, and c can be numbers, variables, or some combination of the two.

Squaring a Trinomial

When we square a trinomial, we square it the same way we would any ordinary number or variable: we multiply it by itself.

(a + b + c)2 = (a + b + c)(a + b + c)

Now, before we go any further, it's important to note that (a + b + c)2a2 + b2 + c2 - an extremely common error.

Okay, now that we've established that, let's look at how to multiply a trinomial by itself. To square a trinomial, we use the following formula:

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ac)

To square a trinomial, all we have to do is follow these two steps:

  1. Identify a as the first term in the trinomial, b as the second term, and c as the third term
  2. Plug a, b, and c into the formula

For example, suppose we wanted to square the trinomial x2 + 3x - 4. First, we'll identify the first term as a = x2, the second term as b = 3x, and the third term as c = -4. Now, we just plug the values into the formula and simplify!


As we said earlier, it's just a matter of multiplying the terms and adding them up.

Origins of the Formula

So, where did this formula come from? Let's take a look at how to derive this formula and, in the process, you may find that you like this pattern for squaring a trinomial better than using the formula itself!

As we said earlier, when we square a trinomial, we are multiplying it by itself:

(a + b + c)2 = (a + b + c)(a + b + c)

Now, to multiply any two algebraic expressions with multiple terms (like a trinomial) together, we follow this pattern:

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