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Like terms can be defined as those terms which contain the same variable which is raised to the same power, whereas unlike terms are those that do not have the same variable and are not raised to the same power. Algebraic terms are those that contain coefficients, variables and constants. Like terms can undergo any algebraic operations such as addition, subtraction, multiplication and division. Unlike terms do not have the property to undergo algebraic operations.
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Keywords Takeaways: Algebraic Equation, Like Terms, Unlike Terms, Polynomials, variables
Like Terms
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In Algebra, the like terms can be defined as those terms which contain the same variable which is raised to the same power, suppose 5x+10x is an algebraic equation where “x” is the same variable with the same power 1. In algebraic terms, the numerical coefficients can only vary. We can connect or combine the like terms in an algebraic equation to simplify the algebraic expressions more easily so that the result is obtained accurately.
- Addition, substraction, multiplication, and, divisions- all these arithmatic equations can be solved by using the like terms.
- Combining the like term can be explained by the process of simplification of the arithmatical expressions.
Like and Unlike Terms
Example: The algebraic equation is 20x+4x Now it is clear that the given equation is like term as the variables and the powers are the same. Hence to simplify the given equation we need to add both the variables i:e 20x+4x = 24x, hence the result.
Also Read:
| Algebraic Identities | Addition of Two Real Numbers |
| Algebraic Operations on Complex Numbers | Algebra Formula |
Unlike Terms
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In Algebra, Unlike terms can be defined as those terms which contain the different coefficients and are not raised to the power. Suppose 5x+10y is an algebraic equation where “x” and “y” are the two different variables and are not raised to the same power. Similarly in equation, 5x + 5x², although the coefficient and variables are the same, they are not raised to the same power. Therefore, they are unlike terms.
- In the case of unlike terms, the coefficients and variables must be differents.
- Variables with different coefficients can be described as unlike algebric terms.
Like and Unlike Terms
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Simplification of Like and Unlike Terms
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Algebraic terms are those elements of an equation or an expression which are separated by ‘+’ or ‘-’ signs.
| Example 1: 4x + 16y We cannot simplify this equation as ‘x’ and ‘y’ are unknown. Let us see another example. Example 2: 2x² + 6x + 4y + 3x + 15x² Now rearrange this expression and rewrite by combining the like terms together: 15x² + 2x²+ 3x + 6x + 4y Now add the like terms, the result will be 17x² + 9x + 4y |
Thus, it can be seen that algebraic terms with the same variables are added together. The addition of these terms was possible only because of the fact that variables in both these examples above are the same even if the numerical terms are different which are added as normal numbers are added and the variable factor remains unchanged. Now, the terms which have the same variables are called like terms.
Thus, terms having the same variables raised to the same power are known as like terms.
So, what is 17x², 9x and 4y called? These are called unlike terms since the variables and raised power of these variables are “unlike” or not the same.
Further simplifications on unlike terms cannot be directly performed. Based on the following examples, it is clear that an algebraic equation consists of terms that can be identified into like terms and unlike terms.
| Example 3: 5xy + 6x² + 20xy +15y² +8x² If you look at the above algebraic equation properly, the terms 5xy and 20xy, as well as 6x²and 8 x² have common variables. Only the numerical values are different. Apart from this, all the variables are the same, so these terms can be added as follows:- 20xy + 5xy = 25xy 6x² + 8x² = 14 x² Because these terms have common variable factors in them and mathematical operations can be performed, they are called like terms. After adding the like terms, consider the expression again. 20xy + 6x² + 5xy + 15y² +8x² = 25xy + 14x² + 15y² |
Now observe the expression again, none of the terms has any common factors between them and no mathematical operations can be performed on them anymore. Therefore, these terms are called, unlike terms.
Read More: Polynomials important questions
Differences Between Like and Unlike Terms
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There are some basic differences between like and unlike terms.
| Like Term | Unlike Term |
|---|---|
| Like term includes same variables and exponents. | Unlike terms includes different variables and exponents. |
| We can simplify the like terms by combining all the variables and exponents of the equation. | We can not simplify the unlilike terms by combining all the variables and exponents of the equation. |
| Like Terms can be added very easily, and it is also known as similar terms. | Unlike Terms can not be calculated easily, and it is also known as dissimilar terms. |
| Addition, subtraction, multiplications, and divisions- all these arithmetic equations can be solved by using the like terms. | In the case of unlike terms, addition, subtraction, multiplications, and divisions can not be done. |
Things To Remember
- Like terms are those terms which have the same variable and same exponent raised to power.
- Unlike terms are those where the coefficients are different in an algebraic equation.
- Like terms can be added easily.
- Unlike terms are not added because of different variables.
- Example of like term:- 3x² + 2x² = 5x²
- Example of unlike terms :- 25xy + 14x² + 15y²
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Sample Questions
Ques: What are like terms? (2 marks)
Ans: In Algebra, the like terms can be defined as those terms which contain the same variable which is raised to the same power, suppose 3x+10x is an algebraic equation where “x” is the same variable with the same power 1. In algebraic terms, the numerical coefficients can only vary. We can connect or combine the like terms in an algebraic equation to simplify the algebraic expressions more easily so that the result is obtained accurately.
Ques: what are algebraic equations? (2 marks)
Ans: Algebraic terms can be defined by taking an example of an equation, so let us suppose that 17x²+3y=7, is an algebraic equation now if we look at this equation we observe that there are three terms in the equation i:e 17x², 3y and 7. Where 17x² and 3y are variables and 7 is a constant. 17x²+3y is an algebraic equation.
Ques: What do you mean by unlike terms? (2 marks)
Ans: The Unlike terms can be defined as those terms which contain the different coefficients and the power of the coefficient are also not the same are termed as, unlike terms. Suppose 5x+10y is an algebraic equation where “x” and “y” are the two different variables and are not raised to the same power.
Ques: Identify whether the following terms are like or unlike. (2 marks)
2x + 7x
6xy + 2y
5x² + 20x
17x² + 24x²
Ans: let us compare the following whether they are like terms or unlike terms
- 2x + 7x is a like term because the coefficient “x” is the same and the powers are also the same.
- 6xy + 2y is an unlike term as the variables are different.
- 5x² + 20x is also an unlike term because of the different variables.
- 17x² + 24x² is a like term.
Ques: Simplify the expressions by collecting the like terms ? (3 marks)
14x² + 4xy + 8x² + 4x + 7xy
Ans: Let us consider the equation 14x² + 4xy + 8x² + 4x + 7xy
Now, lets collect the like terms together and rearrange the following equation
14x² + 8x² + 4xy + 7xy + 4x
Add the like terms
22x² + 4x + 11xy
This equation now cannot be further simplified as the terms are now unlike.
Ques: simplify the expressions :- (2 marks)
15xy + 32 xy
15x² + 2xy + 3x² + 6x + xy
Ans: let us solve the following:-
- 15xy + 32 xy given
Now we can see that the equation is a like equation so the terms can be added simply
Hence, 15xy + 32 xy = 47xy
- 15x² + 2xy + 3x² + 6x + xy given
Now we need to identify and rearrange the equation where like terms are put together
15x² + 3x² + 2xy + xy + 6x
18x² + 3xy + 6x is the desired answer.
Ques: Give examples of like and unlike terms? (2 marks)
Ans: LIKE TERMS
5xy + 2 xy is an example of like terms as we can observe that in the following equation the coefficients are the same and the power is also the same and can be further added and gives the answer as 7xy.
UNLIKE TERMS
2x + 16xy is an example of unlike terms as the coefficients are different and the terms cannot be added any further.
Also Read:
| Straight Lines | Angle Between Two Lines | Zeros of Polynomial |
| Horizontal and Vertical Lines | Conic Sections | Roots of Polynomial |
| Algebra | Integers as Exponents | Addition and subtraction of Integers |
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