# Like and Unlike Algebraic Terms (Definition and Examples)

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Like and Unlike Algebraic Terms
Before getting into like terms and unlike terms, one should be able to distinguish what an algebraic
term is? You can understand this by using an example. 9x + 4y&sup2; = 5 is an algebraic equation. It consists
of 3 terms, i.e. 9x, 4y&sup2; and 5. The first two terms consist of variables and 5 is a constant. 9x + 4y&sup2; is an
algebraic expression. It has two terms 9x and 4y&sup2;. In this article, you are going to learn the definition of
like and unlike algebraic terms in Maths with more examples.
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Like and Unlike Algebraic Terms (Definition and Examples)
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What are Like Terms?
In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the
same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like
terms to simplify the algebraic expressions so that the result of the expression can be obtained very
easily.
For example, 4x + 10x is an algebraic expression with like terms. In order to simplify this algebraic
expression, we can add the like terms. Thus, the simplification of the given expression is 14x. In the same
way, you can perform all the arithmetic operations (https://byjus.com/maths/word-problemsarithmetical-operations/) on the like terms.
What are Unlike Terms?
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Algebraic
terms, which does not have the same literal coefficients, and cannot be raised to the same
power are called, unlike terms.
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Like and Unlike Algebraic Terms (Definition and Examples)
For example, 4x + 9y is an algebraic expression with unlike terms. Because it has two different variables
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Like and Unlike Algebraic Terms Examples
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Algebraic terms are those individual elements in an equation or an expression separated by ‘+’ or ‘-’
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and-unlike-algebraic-terms/)
Consider the expression: 9x + 6y
We cannot simplify this any further as ‘x’ and ‘y’ are unknown. Check out another example.
4x&sup2; + 3x + 4y + 8x + 10x&sup2;
If rearranged, this expression can be re-written as:
10x&sup2; + 4x&sup2;+ 8x + 3x + 4y
= 14x&sup2; + 11x + 4y
Thus, it is seen that algebraic terms with the same variables are added to each other. The addition of
certain terms was possible only because the variables in both these cases are the same even if the
numerical coefficients are different which can be added as normal numbers and the variable factor
remains as it is. Now, these terms which have the same variables are called like terms.
Thus, terms having identical variables raised to the same exponent are like terms.
So, what is 14x&sup2;, 11x and 4y called? These are called unlike terms since the variables or exponent raised to
these variables are “unlike” or not same.
Further operations on unlike terms cannot be directly performed. Based on this, it is clear that an
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be categorized into like terms and unlike terms.
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Like and Unlike Algebraic Terms (Definition and Examples)
Let’s consider another example 2xy + 4x&sup2; + 5xy +5y&sup2; +16x&sup2;
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If you notice properly, the terms 2xy and 5xy, as well as 4x&sup2;and 16 x&sup2; have common factors. Only the
numerical coefficients are different. Apart from that, all the variable factors are the same, so these
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2xy + 5xy = 7xy
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4x&sup2; +16x&sup2; = 20 x&sup2;
Because these terms have the variable factors in common and an arithmetic operation can be
performed on them, they are called like terms. After adding the like terms, consider the expression
again.
2xy + 4x&sup2; + 5xy + 5y&sup2; +16x&sup2; = 7xy + 20x&sup2; + 5y&sup2;
If you observe the expression now, none of the terms has any common factors and no arithmetic
operation can be performed on them further. These terms are called, unlike terms.
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