Like and Unlike Algebraic Terms

Before jumping to the like and unlike terms let’s understand what an algebraic term is? Let’s understand it by an example. 5x + 3y² = 12 is an algebraic equation. It consists of 3 terms i.e. 5x, 3y², and 12. The first two terms consist of variables and 12 is a constant. 5x + 3y² is an algebraic expression. It has two terms 5x and 3y². In this article, we are going to learn the like and unlike algebraic terms.

Like Terms

These are the terms with the same variables and each of the variables having the same exponent power on them. One can combine the like terms to simplify the algebraic expressions so that the result of the expression can be calculated very easily. For example, 3y + 5y 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 8y. In the same way, one can perform all the arithmetic operations on the like terms.

Examples

Here, each of the terms has the same variables and the same power. 

1. 40xy² & 56xy²: In the first example xy² is the common coefficient for both terms. So, they fall into the category of like variables.
2. 30z² & 18z²: Here z² is the common coefficient for both terms. So, they fall into the category of like variables.
3. 45abc & 29abc: Here abc is the common coefficient for both the terms. So, they fall into the category of like variables.
4. 18r³ & 38r³: Here r³ is the common coefficient for both terms. So, they fall into the category of like variables.
5. 2xy & 8xy: Here xy is the common coefficient for both the terms. So, they fall into the category of like variables.

Unlike Terms

These are the terms with different variables and each of the variables having a different exponent power on them. For example, 9x + 6y is an algebraic expression with unlike terms. Because it has two different variables x and y, and not raised to the same power.

Examples

1. 40xy² & 56xy: Here, One has variables xy² and the other has variables xy. Both have the same variables but with different exponents related to them. So, they fall into the category of unlike terms.
2. 30z² & 18z: Here, One has variables z² and the other has variables z. Both have the same variables but with different exponents related to them. So, they fall into the category of unlike terms.
3. 45abc & 29ab: Here, One has variables abc and the other has variables ab. Both have different variables related to them. So, they fall into the category of unlike terms.
4. 18r³ & 38r: Here, One has variables r³ and the other has variables r. Both have the same variables but with different exponents related to them. So, they fall into the category of unlike terms.
5. 2xy & 8x: Here, One has variables xy and the other has variables x. Both have different variables related to them. So, they fall in the category of unlike terms.

Below are a few examples to make these two terms more clear.

Question 1. Identify like and unlike terms from the given terms:  3x, 5xy, 18x²y, 5x³, 29xy, 50x³?

Solution:

Like terms: (5xy, 29xy), (5x³, 50x³)

Unlike terms: 3x, 18x²y

Question 2. Find like terms for 67x³ from the given terms: 3x, 5xy, 18x²y, 5x³, 29xy, 50x³?

Solution:

Like terms: 5x³, 50x³

Question 3. Find unlike terms for 67x³ from the given terms: 3x, 5xy, 18x²y, 5x³, 29xy, 50x³?

Solution:

Unlike terms:  3x, 5xy, 18x²y, 29xy.

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