Like and Unlike Algebraic Terms: Like and Unlike Algebraic Terms Examples

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is an algebraic equation. It consists of 3 terms i.e. . The first two terms consist of variables and 5 is a constant. is an algebraic expression. It has two terms

Like and Unlike Algebraic Terms

Like and Unlike Algebraic Terms

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What Are like Terms?

Like terms are defined as the terms that contain the same variable which is raised to the same power. In 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, is an algebraic like term. In order to simplify the algebraic expression, we can add the like terms. Thus, the simplification of the given expression is . In the same way, we can perform all the arithmetic operations on the like terms.

What Are Unlike Terms?

An algebraic term, which does not have the same literal coefficients, and cannot be raised to the same power is called, unlike terms.

For example, is an algebraic unlike term. Because it contains two different variables x and y, and it cannot be raised to the same power.

Like and Unlike Algebraic Terms Examples

Therefore, algebraic terms are those individual elements in an equation or an expression separated by ‘+’ or ‘-’ signs.

Consider the expression:

We cannot simplify this any further as ‘x’ and ‘y’ are unknown. Check out another example.

If rearranged, this expression can be re-written as

which is equal to

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.

1 and 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 algebraic expression consists of terms which can be categorized into like terms and unlike terms.

Example

Here terms 2xy and 5xy, as well as 4x²and 16 x² have common factors. Only the numerical coefficients are different. Apart from that, all the variable factors are the same, so these terms can be added

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.

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.

Example 1: In the algebraic expression

Solution:

Here given expression,

Like terms:

Because the term having the same variable with same exponents.

Unlike terms:

Because the term having the same variable with different exponents or different variable with same exponents.

Example 2: In the algebraic expression

Solution:

Here given expression,

Like terms: ,

Unlike terms: and ,