Working with Binomials


Last updated on by ​Arikaran


Binomials

What is a Binomial?

  • A binomial is an expression that has a total number of two terms (prefix bi- means two root word nominal means name or term).
  • A term is a number or a product of numbers and variables.

Here are some examples of binomials:

Binomial

In each example, we only have a 1st and 2nd term making them binomials. Now let’s look at different problems we can find binomials in.

Adding and Subtracting with Binomials

1) Adding Binomials

When adding two or more binomials, simply collect like terms and then add them together.

Like terms: Terms that have the same variable to the same power.  Let’s try some examples.

#1

(2x+7)+(9x+15)

To begin this question, we can first drop the parenthesis since each binomial is not being affected by a factor outside of it. So now we have

2x+7+9x+15

Now all we must do is collect like terms and simplify

2x+7+9x+15

2x+9x+15+7

11x+22

Done!

#2

(10x^2+14x)+(3x+6)

In this example, we will start by once again dropping the parenthesis.

10x^2+14x+3x+6

We can see that we only have one set of like terms. In this case, they are terms that contain the factor of x

10x^2+14x+3x+6

10x^2+17x+6

Done!

#3

(m^2+8n^2)+(3m^2+6)

Since we are only adding the binomials, we can drop the parentheses

m^2+8n^2+3m^2+6

Next, we can combine like terms

m^2+8n^2+3m^2+6

4m^2+8n^2+6

Notice: 

Even though the n and m are raised to the power of 2, they cannot be combined. Like terms must have the same variable to the same power to be like terms.

Done!

Watch out for the next article about subtracting binomial.


Author: Mr. Vernon Sullivan, is a tutor at FPLA Miami, FL HQ premier 1-on-1 tutoring center. He teaches Algebra, Geometry, Pre-Cal, ACT, SAT, SSAT, HSPT, PERT, ASVAB and other test prep programs.

Mrs. Emimmal Sekar Proofread this article. Mr. Arikaran Kumar manages the website and the social media outreach.

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