Like and Unlike Algebraic Terms
2026-02-28 09:54 Diff
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Last updated on October 29, 2025

In algebra, expressions consist of terms separated by addition or subtraction. A term can include numbers, variables, or both. Identifying like and unlike terms helps simplify and solve algebraic expressions.

What are Like Terms?

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3x2 and 5x2 are like terms because both have the variable x2.

2xy and −7xy are like terms because both have the variable xy.

What are Unlike Terms?

Unlike terms are defined as terms with different variables, or the same variables with different exponents.

For example:

4x and 4y are unlike terms because they have different variables.

3x2 and 3x are unlike terms because the terms have different exponents.


ab and a2b are unlike terms because they have different powers of a.

Difference Between Like and Unlike Terms

The variables and their powers decide whether two terms are like or unlike. Understanding the difference between them helps us simplify and solve algebraic expressions.
 

Feature

Like terms

Unlike terms

Definition

Terms that have the same variables raised to the same exponents.

Terms that have different variables, or the same variables with different exponents.

Example

2x and 3x; 4xy and 5xy

3x and 3y; 5x3 and 5x

Can the terms combine?

Yes, like terms can be added or subtracted.

No, unlike terms cannot be combined directly.

Simplification

Can be easily simplified by combining coefficients.

Cannot be simplified unless rewritten as like terms. 

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Rules of Addition and Subtraction of Like Terms

Like terms can be added or subtracted easily by following these simple steps:

Step 1: Identify like terms these are terms that have the same variables with the same exponents. Once identified, you can add or subtract their coefficients. For example,\( 2x + 3x = 5x\).

Step 2: Add or subtract the coefficients of like terms while keeping the variable unchanged. For example, \(6y + 3y = (3 + 6) y = 9y.\)

Step 3: Keep the sign in mind, pay attention to the signs (+/−) of each term when adding or subtracting. \(10y -15y = -5y.\)

Rules of Addition and Subtraction of Unlike Terms

Unlike, terms cannot be added or subtracted because they have different variables or different exponents, making them impossible to combine. Here’s how to handle them: 

Step 1: Do not combine unlike terms. Instead, leave them as they are. For example, \(3x + 7y\) cannot be simplified, so it stays as it is. 

Step 2: Write them in a simplified and organized manner, without combining them.

Tips and Tricks of Like and Unlike Algebraic Terms

Learning about like and unlike terms helps make algebra easier to understand. These simple tips and tricks will help students quickly identify, group, and simplify terms while solving math problems.
 

  • When identifying like terms, always check the letters and their powers, not the numbers.
  • Terms are “like” only if both the variable(s) and their exponents match exactly.
  • If the variable part changes (like a and b), they are unlike terms.
  • You can add or subtract like terms but never unlike ones.
  • When combining terms, remember to include the positive or negative sign before each term.

Common Mistakes in Like and Unlike Algebraic Terms and How to Avoid Them

Understanding the difference between like and unlike terms in algebra is important. But many students find it hard and make simple mistakes that lead to wrong answers. Here are some common mistakes with tips to avoid them:

Real-Life Applications of Like and Unlike Algebraic Terms

Like and unlike terms aren’t just for solving equations in class; they also help us to solve practical, real-life problems. Here are some real-life applications of like and unlike algebraic terms.  

  • Budgeting and Finances: When creating a monthly budget, expenses like rent, groceries, and travel are unlike terms because they represent different categories. But if your child has several grocery bills, those can be added together as like terms since they belong to the same category.
  • Construction and Architecture: Workers use like and unlike terms to stay organized. For example, in construction, cement bags of the same type can be counted together just like combining like terms. Materials that are different can’t be grouped together, as they are unlike terms. This helps workers plan better and avoid mistakes during construction.
     
  • Classroom Seating or Grouping: In a classroom, students in the same team are grouped together, like combining like terms. Students from different teams stay separate, just like unlike terms, helping organize seating easily
     
  • Distance or Travel Planning: When planning a trip, distances in the same units and along the same route can be added easily, like combining like terms. Distances in different units are unlike terms and can’t be added directly.
  • Inventory or Stock Counting (Like Terms): In shops, similar items are grouped together, like combining like terms in math. Items of the same type, such as pens, can be added easily, while different ones, like pens and pencils, are counted separately.

Download Worksheets

Problem 1

Are the terms 4x, −7x, and 9x like terms?

Okay, lets begin

 Yes, the terms are like terms.
 

Explanation

All three terms have the same variable, which is x raised to the same power. Only the coefficients are different.
 

Well explained 👍

Problem 2

Simplify: 3a + 7a

Okay, lets begin

 10a
 

Explanation

Both terms have the same variable a, they are like terms. Add the coefficients:
3 + 7=10 and add the variable a.
 

Well explained 👍

Problem 3

Simplify: 8x −5x

Okay, lets begin

3x
 

Explanation

They are like terms with the same variable x. So subtract coefficients:
8x − 5x = 3x
 

Well explained 👍

Problem 4

Simplify: 2x + 3y

Okay, lets begin

 It is an unlike term.
 

Explanation

x and y are different variables, so they are unlike terms and cannot be combined.

Well explained 👍

Problem 5

Simplify: 4x + 3y + 5x + 2y

Okay, lets begin

 (4x + 5x) + (3y + 2y) = 9x + 5y
 

Explanation

Here, we need to group terms with the same variable. 4x and 5x have the same variable (x), so group them together. Similarly, 3y and 2y are grouped together.

Once the grouping is done, we can add the like terms. Grouping and adding only like terms gives us the answer 9x + 5y, which cannot be simplified further.

Well explained 👍

FAQs of Like and Unlike Algebraic Terms

1.How do we find like and unlike algebraic terms?

To find the like and unlike algebraic terms, look at the variables and their powers. Like terms have the same variables with the same exponents. If they have different variables or the same variables with different powers, then they are unlike terms. 
 

2.Can we combine unlike algebraic terms?

No, we cannot combine unlike algebraic terms.
 

3.Are 9x and 4y like terms?

No, they are unlike terms.
 

4.Are like terms important in algebra?

Like terms help to simplify the expressions and solve the equations by combining them using operations like addition or subtraction.
 

5.Are 5x2y and 7yx2 like terms?

Yes, the variables and their powers are the same, even though the order is different.
 

6.How can parents guide their child to identify like terms correctly?

Parents can encourage their child to look closely at the variable part. If both the variable and its power are the same, they belong to the same group of like terms.

7.What can parents do if their child finds variables confusing?


Parents can explain that variables like x or y are simply placeholders for numbers, just like using letters to represent unknowns in a word puzzle.

8.How can parents explain unlike terms to their child in a simple way?


Parents can say that unlike terms are like “different types of fruits” you can’t add apples and oranges, just like you can’t add 3x and 5y.

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.