What is Term In Math? And How Does it Works?

Are you unable to solve algebraic problems? Or do you get stuck while solving the equation? Well, this might be because you are unable to identify like and unlike terms. 

Excuse me!!! I do not have any idea regarding what is term in math? 

Do not worry! I have explained all the details that will help you clear your doubts regarding terms in math and allow you to know how to analyze terms in algebraic equations. 

But before that, let me explain to you what are the key components of an algebraic equation.

There are four key components of an algebraic equation, that is

Terms: We have discussed it below.
Coefficients: The integer multiplied with the single or multiple terms’ variable of the algebraic equation.
Variable: It is the letter, or a symbol uses to represent a value.
Constant: It is a number or the value, which can not be changed in expression. 

What is term in math?

The term can be a variable, a number. Moreover, it is the product of two or multiple variables or even a variable and a number. The algebraic expression or equation is made up of single or multiple terms. 

Let’s take an example of it

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4x = 0 (single term)

4x-y = 0 (two terms that are 4x and y)

Keep in mind that the terms are summed up to make an equation. Like 5xy has the product of 5, x, and y. Moreover, take another term as -2z that is the product of z and -2. 

Now, combine both terms that are 5xy and -2z as:

=> 5xy + (-2z)

=> 5xy-2z (This is known as an algebraic equation)

Depending on the variables and the powers, the terms are classified into 2 terms, that is:

  • Like algebraic terms
  • Unlike algebraic terms

What are the key factors of terms to keep in mind?

Once you understand the basic definition of what is term in math, you need to understand the 4 key factors of terms. That is:

  • The variables or the numbers, which are multiplied to make a term, are known as factors. For instance, 4xy is the term that has three factors as 4, x, and y.
  • If the term has the power, then the factor of terms is taken as 3x^2 => 3, x, and x that is 3 factors.
  • The factors never are further factorized. For instance, 4ab can not be factorized as 4 and ab or 4a and b as ab can factorize as a and b.
  • 1 can not consider as a separate factor.

What are like and unlike terms?

If you want to know what is term in math, it is always necessary that you must know what are like and unlike terms. So, understand both one by one.

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Like terms

In an algebraic expression or equation, the like terms consist of the same variable with the same power. But remember that the coefficients of the like terms can vary. 

You can easily make combinations of the like terms to simplify the algebraic equation by which the result of the equation is easily obtained. 

Let’s take an example of like terms

Suppose you have an equation as 5x-3x. As you can see that 5x and 3x have the same variable ‘x’ that is separated by the operator ‘minus.’ 

Now, to simplify the equation, you can subtract 3x from 5x, which will give 2x. This is how you can solve the like terms in an equation.

Unlike terms

Algebraic terms are the terms that do not have the same variable with similar or dissimilar power. Moreover, these terms need to solve individually.

Let’s take an example of it

Suppose you have the equation as 3a – 5b. Here, there are two different variables. Moreover, these terms have the same power.

Always remember that you can not use the combining like terms for dividing and multiplying. 

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Can we solve like and unlike terms? If yes, then how?

Yes, you can solve like and unlike terms.

Moreover, it is quite easy to solve the like and unlike terms. But before solving them, you must remember what is term in math. This will help you to solve terms with ease.

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So, let’s check how to analyze terms (like and unlike terms) in algebraic equations.

Suppose you and your other 10 friends went to a restaurant to eat some snacks. And all of you gave the order as (consider friends name as 1, 2, 3, and so on):

  • 1 ordered: Hamburger
  • 2 ordered: Hamburger
  • 3 ordered: French fries 
  • 4 ordered: Soft drink
  • 5 ordered: Hamburger
  • 6 ordered: Hamburger
  • 7 ordered: Hamburger
  • 8 ordered: French fries
  • 9 ordered: French fries
  • 10 ordered: Soft drink
  • You: Soft drink

You can see three similar or like snacks: Hamburger, French Fries, and Soft drinks. Now, you can separate them as like and unlike terms.

The unlike terms are Hamburger, French Fries, and Soft drinks.

Separate like and unlike terms and it will look as:

The equation can be written as: 

=> 2h+f+d+3h+2f+2d

Simplify it as:

=> 5h+3f+3d

This is what is term in math, and how does it get solved? 

Now, let’s test whether you have understood what is term in math or not!!!

How many terms, like terms, and unlike terms, are there in the following equations:

  1. 9x + 6y
  2. 4 x² + 3x + 4y + 8x + 10x²
  3. 3abc
  4. -5x²
  5. a − b


There are 2 terms in the equation 9x + 6y is 9x and 6y. But there are no like terms, although it has 2 unlike terms with variable x and y.
There are 5 terms in the equation 4x² + 3x + 4y + 8x + 10x². But there are 2 like terms, although it has 3 unlike terms. But once it is simplified, it will be => ( 4x² + 10x²) + (3x + 8x) + (4y) => 14x² + 11x + 4y. There are 3 terms with no like terms, although it has 3 unlike terms with variable x², x, and y.
There is 1 term in equation 3abc. But there are no like and unlike terms, as it has no other terms to get compared.
There is 1 term in equation -5x². But there are no like and unlike terms, as it has no other terms to get compared.
There are 2 terms in the equation a – b is a and b. But there are no like terms, although it has 2 unlike terms with variables a and b.

Let’s wrap it up!!

It is quite essential to understand what is term in math as without understanding terms, you can not solve algebraic equations. I have simplified the method of how you can analyze the terms of an equation. 

Once you get familiar with the terms, you can easily combine like and unlike terms. If you still have any doubt or looking for more practice questions, please let me know through your comments. Moreover, I will definitely help you with the best practice questions and best guide about terms in math writing assignments. Also, get the best mathematics assignment help to clear your further doubts.

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