Like and Unlike Algebraic Terms: Definition and Examples (original) (raw)
Last Updated : 23 Jul, 2025
Like terms are terms in algebraic expressions that have the same variables raised to the same powers. Like and Unlike Terms are the types of terms in algebra, and we can differentiate between like and unlike terms by simply checking the variables and their powers. We define algebraic terms as the individual terms obtained from the algebraic equation.
For example in the algebraic equation **5x + 3y 2 **= 12 we have three terms that are, 5x, 3y², and **12. Here, **5x, and 3y 2 are variable terms and 12 is the constant term. The below image shows the like and unlike terms.
In this article, we will learn about Like Terms, Unlike Terms, their Examples, Simplification, and others in detail.
**Like Terms
Like terms are the terms that have the same variables and the power of each of the variables is also the same. We can combine like terms to simplify the algebraic expressions, and this can be calculated very easily. For example, 3y + 5y is an algebraic expression with like terms 3y and 5y. In order to simplify this algebraic expression, we add the like terms. Thus, the simplification of the given expression is 8y.
Examples of Like Terms
Like terms, are the terms that have the same variable with similar power. Some examples of the like terms are,
- **40xy 2 and 56xy 2 : In the first example xy2 is the common coefficient for both terms. So, they are like terms.
- **30z 2 and 18z 2 : z2 is the common coefficient for both terms. So, they are like terms.
- **45abc and 29abc: abc is the common coefficient for both terms. So, they are like terms.
- **18r 3 and 38r 3 : r3 is the common coefficient for both terms. So, they are like terms.
- **2xy and 8xy: xy is the common coefficient for both terms. So, they are like terms.
Addition and Subtraction of Like Terms
We can easily perform addition and subtraction of like terms and it do not require any special rule they are generally simplified using the normal addition and subtraction rules. We can understand this concept using the following example.
**Example: Simplify 11x 3 + 5x 3
**Solution:
As we see that these are like term because they have similar variables and their power is also constant.
We can easily add these terms directly.
= 11x3 + 5x3
= 16x3
This is possible because they have the same variables with similar power and this can be understood as, we can directly add rupees to rupees, i.e. 5 Rs + 7 Rs is 12 Rs. But we can not directly add rupees with dollars and 5 Rs + 7 Dollars can not be directly simplified.
Similarly, we can also subtract like terms directly just add we add like terms this can be understood by the following example.
**Example 1: Simplify 11x 3 - 5x 3
**Solution:
As we see that these are like term because they have similar variables and their power is also constant.
We can easily subtract these terms directly.
= 11x3 - 5x3
= 6x3
**Example 2: Add 3 x **+ 2 y **+ 5 and 4 x **− 3 y **+ 7.
**Solution:
(3__x_ + 2__y_ + 5) + (4__x_ − 3__y_ + 7)
= (3__x_ + 4x) +(2y + (-3y))+ (5 + 7)
= 7__x_ − _y + 12
Unlike Terms
Unlike Terms are terms with different variables and each of the variables may or may not have different exponents on them. For example, 9x + 6y is an algebraic expression with, unlike terms. Because it has two different variables x and y.
If the variables are different we do not check the power as they are in any way unlike terms but if the variables are the same we check for their powers because they may or may not be like terms.
Such as 5x2 and 6x2 are like terms but, 5x2 and 6x3 are unlike terms.
Examples of Unlike Terms
Unlike terms, are the terms that do neither have the same variables nor similar power. Some examples of unlike terms are,
- **40xy 2 and 56xy: Here, in one algebraic expression the variable is xy2 and in the other algebraic expression the variable is xy. Both variables are the same but have different powers. So, they are unlike terms.
- **45abc and 29ab: Here, in one algebraic expression the variable is abc and in the other algebraic expression the variable is ab. Both variables are different. So, they fall into the category of, unlike terms.
Addition and Subtraction of Unlike Terms
Addition and subtraction are not performed between, unlike terms, i.e. we can not add or subtract unlike terms and this can be understood by the example as we can not add 5 liters of milk with 6 kg of rice. In the same way, we can not add or subtract, unlike terms.
For example, 3xy + 5x can not be further solved and it is left in the same way.
Difference Between Like Terms and Unlike Terms
The differences between the like terms and, unlike terms are discussed in the table below.
| Feature | Like Terms | Unlike Terms |
|---|---|---|
| Definition | Like terms are the terms that have the same variables and the same exponent values. | Unlike terms are terms that have different variables and exponents. |
| Simplification | We can easily simplify the like terms. | Unlike terms that can not be simplified. |
| Combining terms | Like terms can be combined directly to make calculation. | Unlike terms cannot be combined directly because they represent different quantities |
| Addition or Subtraction | Addition and subtraction can be achieved in Like terms. | We cannot add or subtract, unlike terms. |
| Examples | Examples of Like terms are, x2, 5x2, -11/3x2, etc. | Examples of Unlike terms are, x2y, 5x3, -11/3x, etc. |
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Examples for Like and Unlike Algebraic Terms
**Example 1: Identify like and unlike terms from: 3x, 5xy, 18x 2 y, 5x 3 , 29xy, 50x 3
**Solution:
Like and Unlike terms from the given terms are,
**Like Terms: (5xy, 29xy), and (5x3, 50x3)
**Unlike Terms: 3x, 18x2y
**Example 2: Simplify 3xy + 5x 2 + 11ab - 4xy
**Solution:
Given Expression:3xy + 5x2 + 11ab - 4xy
Like term in the given expression, 3xy and -4xy
On simplifying,
= 3xy - 4xy + 5x2 + 11ab
= -xy + 5x2 + 11ab
Rest all the terms are unlike terms so they can not be further solved.
**Example 3: Simplify 8x + 15x 2 + 11x - 4x 2
**Solution:
Given Expression: 8x + 15x2 + 11x - 4x2
Like term in the given expression, (8x, 11x) and (15x2, -4x2)
On simplifying,
= 8x + 11x + 15x2- 4x2
= 19x - 11x2
Rest all the terms are unlike terms so they can not be further solved.