Like and Unlike Algebraic Terms
In mathematics, algebraic expressions mean an expression that consists of both variables and constants together along with the arithmetic operation such as addition, subtraction, multiplication, and division. For example: 3x +19y = 30 is an algebraic expression as it consists of three terms i.e. 3x, 19y, and 30. The first two terms i.e. 3x and 19y, where x and y are variables whereas 30 is a constant. Therefore, algebraic terms are individual elements in an expression that are separated by the plus or minus signs. There are two types of algebraic terms  Like and unlike algebraic terms. Let us see the meaning of like and unlike algebraic terms along with a few examples.
1.  Definition of Like Terms 
2.  Definition of Unlike Terms 
3.  Solved Examples for Like and Unlike Algebraic Terms 
4.  Practice Questions 
5.  FAQs on Like and Unlike Algebraic Terms 
Definition of Like Terms
Like terms are those terms whose variables and their exponent power are the same. The coefficient of these variables can be different. Algebraiclike terms are terms that are similar to each other. These like terms in the algebraic expression can be combined to simplify the expression to derive the answer in a simple manner. For example, This is a like algebraic expression 8y + 2y where y is the same variable in the expression and the coefficients are different. To simplify it further, we can add the two like terms i.e. 8y + 2y = 10y. Hence, all arithmetic operations such as addition, subtraction, multiplication, and division can be performed only on like algebraic terms.
Consider another expression 10x^{2 } 4x^{2}, here we see that the variables have the same exponent but the coefficients are different. We can further simplify this expression by subtracting the same variables from each other. This is possible since the variables and the exponents are the same irrespective of the coefficients being different. The coefficients can be considered as normal numbers along with variables and exponent value, which remain the same after subtraction. Hence, after simplifying the expression we get 10x^{2}  4x^{2} = 6x^{2}
The process of simplifying the expression is known as combining like terms.
Definition of Unlike Terms
Unlike terms are those terms whose variables and their exponents are different from each other. In an expression, the coefficient is different, the variables are different i.e 2 variables, and the exponent powers are different, that expression is known to obtain, unlike terms. For example, the algebraic expression 3x + 9y where x and y are two different variables with different coefficients is known as, unlike algebraic terms.
The simplification of expressions or combining like terms cannot be done on unlike terms, as the variables and exponents are not similar. For example, 8xy + 6y  9x  10x^{2}, as seen here, there are different variables, exponents, and coefficients. This expression cannot be simplified as all the terms are different from each other.
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Solved Examples for Like and Unlike Algebraic Terms

Example 1: In the algebraic expression, identify the like terms  10xy + 3x^{3} + 21xy + 2x  xy  6 and simplify it.
Solution: Given expression:10xy + 3x^{3} + 21xy + 2x  xy  6
like terms: 10xy + 21xy  xy (as the variables are the same irrespective of the coefficient is different)
Therefore, the like terms are simplified as 10xy + 21xy  xy = 30xy.

Example 2: In the algebraic expression, identify the unlike terms  32x^{2}  7y + 4x^{2} + 43x^{2}  5xy  12x
Solution: Given expression 32x^{2}  7y + 4x^{2} + 43x^{2}  5xy  12x
unlike terms: 7y  5xy  12x are unlike terms(as the variable and coefficients are different from each other.)

Example 3: What is the final expression from this algebraic expression after combining like terms? 4xy + 15x^{2} + 50xy + 11x^{2}  70y^{3}  25y
Solution: From the given expression, first let's find out the like terms and the unlike terms
Like terms: 4xy + 50xy + 15x^{2} + 11x^{2}
Unlike terms: 70y^{3}  25y
The final expression can be derived by combining the like terms. Hence, 4xy + 50xy + 15x^{2} + 11x^{2} = 54xy + 26x^{2}
Therefore, the final expression is 54xy + 26x^{2 }+ 70y^{3}  25y
FAQs on Like and Unlike Algebraic Terms
What are Like and Unlike Algebraic Terms?
Like algebraic terms are those terms whose variables and their exponent power are the same. The coefficient of these variables can be different. Algebraiclike terms are terms that are similar to each other. These like terms in the algebraic expression can be combined to simplify the expression to derive the answer in a simple manner. For example: 12x  6x, where x is the variable and 12 and 6 are the different coefficients.
Unlike algebraic terms are those terms whose variables and their exponents are different from each other. In an expression, the coefficient is different, the variables are different i.e 2 variables, and the exponent powers are different, that expression is known to obtain, unlike terms. For example, 3z  8x, where z and x are 2 variables and 3 and 8 are the coefficients.
How do we find Like and Unlike Algebraic Terms?
In a given algebraic expression, if the variables are the same irrespective of different coefficients along with the exponents being similar, those terms are called like terms. Whereas, if an expression consists of two different variables, different exponents, and different coefficients, that expression is known to have unlike algebraic terms. For example: Consider this expression 7xy + x  9y + 13xy  8x + 12z^{2} we can differentiate like and unlike algebraic terms. The like terms are 7xy + 13xy + x 8x which can be simplified further to 20xy  7x. The, unlike terms, are 12z^{2}  9y.
Can we Add or Subtract Like and Unlike Algebraic Terms?
We can add or subtract any number of like algebraic terms. Terms that do not have the same variables are called unlike algebraic terms. An expression with unlike terms cannot be added or subtracted. For example: 7a  46z , 5x^{3} + 45xy , 32z + xy + 12, all these three expressions contain two unlike terms.
What does Combining Like Algebraic Terms Mean?
Combining like terms means, when an algebraic expression consists of like terms i.e. same variables, that expression can be further simplified to a point where no further calculation is required. After combining the like terms, an expression can be solved easily. For example: 5x  10y + 34x + 2y  3xy can be further simplified to 39x  8y 3xy.
Can we Combine Unlike Algebraic Terms?
No, unlike algebraic terms in an algebraic expression cannot be combined or simplified further as the expression consists of two different variables.
What is the difference between Like and Unlike Algebraic Terms?
The differences between Like and Unlike Algebraic Terms are:
Like Algebraic Terms  Unlike Algebraic Terms 
Expression with same variables  Expression with different variables 
Can be further simplified by combining the like terms  Cannot be further simplified by combining unlike terms 
Can add and subtract like algebraic terms  Cannot add and subtract unlike algebraic terms 