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# Difference Between Like and Unlike Terms

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## What are Like and Unlike Terms: Introduction

To differentiate between like and unlike terms: Like and unlike terms play a crucial role in simplifying and manipulating algebraic expressions. Like terms are those that have the same variable raised to the same power. They can be combined by adding or subtracting their coefficients while keeping the variable and its power unchanged. For example, 3x and 5x are like terms because they both have the variable x raised to the power 1. On the other hand, unlike terms have different variables or the same variable raised to different powers. They cannot be directly combined but can be simplified by rearranging or factoring. Understanding the distinction between like and unlike terms is essential for performing operations such as addition, subtraction, multiplication, and division of algebraic expressions, leading to efficient problem-solving in various mathematical contexts. Read further for more detail.

Last updated date: 22nd Sep 2023
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## What is Like Terms?

Like terms in mathematics refer to algebraic terms that have the same variable(s) raised to the same power(s). These terms can be combined by adding or subtracting their coefficients while keeping the variables and their powers unchanged. For example, 3x and 5x are like terms because they both have the variable x raised to the power 1. Similarly, 2x² and -4x² are also like terms because they have the variable x raised to the power 2. By identifying and grouping like terms, we can simplify algebraic expressions and perform operations more efficiently, leading to clearer mathematical equations and solutions. The characteristics of like terms are:

• Same Variables: Like terms have the same variables. For example, terms such as 3x and 5x are like terms because they both have the variable x.

• Same Exponents: Like terms have the same exponents attached to their variables. For instance, 2x² and -4x² are like terms because they both have the variable x raised to the power 2.

• Coefficients: Like terms can have different coefficients, which are the numerical factors multiplying the variables. In like terms, the coefficients can be added or subtracted while keeping the variables and their exponents unchanged.

• Combination: Like terms can be combined by adding or subtracting their coefficients, while keeping the variables and their exponents unchanged. This simplification process helps in performing operations and solving equations more efficiently.

• Algebraic Manipulation: The presence of like terms allows for algebraic manipulation, such as factoring, simplifying expressions, and solving equations, leading to clearer mathematical representations and solutions.

## What is Unlike Terms?

Unlike terms in mathematics refer to algebraic terms that have different variables or the same variable raised to different powers. Unlike terms cannot be combined directly by adding or subtracting their coefficients. For example, 3x and 5y are unlike terms because they have different variables, x and y. Likewise, 2x² and -4x³ are unlike terms because they have the same variable, x, but raised to different powers, 2 and 3. While unlike terms cannot be simplified or combined directly, they can be rearranged, factored, or manipulated in other ways to simplify algebraic expressions and solve mathematical problems. The characteristics of unlike terms are:

• Different Variables: Unlike terms have different variables. For example, terms such as 3x and 5y are unlike terms because they have different variables, x and y, respectively.

• Different Exponents: Unlike terms can have the same variable but raise to different powers. For instance, 2x² and -4x³ are unlike terms because they have the same variable, x, but raised to different powers, 2 and 3.

• Incompatibility for Direct Combination: Unlike terms cannot be directly combined by adding or subtracting their coefficients, as they involve different variables or variable powers.

• Manipulation Possibilities: Unlike terms often require further algebraic manipulation such as rearranging, factoring, or expanding to simplify expressions or perform operations.

• Distinct Mathematical Significance: Unlike terms represent different mathematical quantities or variables, making them distinct entities that cannot be easily merged or simplified together.

## Differentiate Between Like and Unlike Terms

 S.No Category Like Terms Unlike Terms 1 Variables Same Different 2 Exponents Same Different 3 Coefficients Can be added or subtracted Cannot be directly combined 4 Combination Add or subtract coefficients while keeping variables and exponents unchanged Cannot be directly combined 5 Algebraic Manipulation Can be simplified and combined easily Require further manipulation (rearranging, factoring, expanding, etc.) 6 Mathematical Significance Represent the same mathematical quantity Represent different mathematical quantities or variables

By comparing the characteristics of like and unlike terms in a tabular form, it becomes easier to understand the distinctions between them and how they affect algebraic operations and simplification.

## Summary

Like terms in mathematics are terms that have the same variables raised to the same powers. They can be combined through addition or subtraction by simply adding or subtracting their coefficients while keeping the variables and exponents unchanged. On the other hand, unlike terms have either different variables or the same variable raised to different powers. Unlike terms cannot be directly combined, but they can be simplified or rearranged to identify like terms and perform algebraic operations. The difference of two like terms is another like term. When subtracting two like terms, the variables and exponents remain the same, and only the coefficients are subtracted. Whereas, the difference of two unlike terms is not defined in the same way as like terms. Unlike terms have either different variables or the same variable raised to different powers. Therefore, they cannot be directly subtracted.

## FAQs on Difference Between Like and Unlike Terms

1. Can like terms have different exponents?

No, like terms cannot have different exponents. In mathematics, like terms are defined as algebraic terms that have the same variables raised to the same powers. The exponents indicate the power to which the variable is raised. For terms to be considered like terms, they must have the exact same exponents attached to their variables. For example, 3x² and 5x² are like terms because they both have the variable x raised to the power 2. However, 3x² and 5x³ are unlike terms because they have different exponents (2 and 3, respectively) attached to the variable x.

2. Can you add or subtract, unlike terms?

No, unlike terms cannot be directly added or subtracted. Unlike terms have either different variables or the same variable raised to different powers. Since they lack the necessary common factors to combine algebraically, addition or subtraction is not possible without further manipulation. To perform operations involving unlike terms, one must first simplify or rearrange the expressions by factoring out any common factors or by using other algebraic techniques. Once the expressions are simplified and like terms are identified, addition or subtraction can be performed on the like terms to obtain the desired result.

3. What are the properties of like terms?

Firstly, like terms have identical variables, meaning they contain the same letter or symbol representing the variable. Secondly, like terms possess the same exponents attached to their variables. This implies that the variables are raised to the same power. Thirdly, the coefficients of like terms can be added or subtracted while keeping the variables and exponents unchanged. This property allows for the combination and simplification of like terms. By grouping together like terms, algebraic expressions can be condensed and manipulated more effectively.

4. Can variables in like terms have different letters?

No, variables in like terms cannot have different letters. Like terms are characterised by having the same variables, meaning they must use the exact same letter or symbol to represent the variable. For example, 3x and 5y are not like terms because they have different variables, x and y, respectively. In like terms, the variables must be identical, ensuring that they represent the same quantity or unknown value. Having different letters would imply different variables and, therefore, such terms would not meet the criteria to be considered like terms.

5. Can constant terms be considered like terms?

Yes, constant terms can be considered like terms. Like terms are not limited to variables alone, but they can also include constant terms. Constant terms are those that do not contain any variables. Since they lack variables, their exponents are considered to be zero. When two constant terms have the same numerical value, they can be regarded as like terms. For example, 3 and -3 are like terms because they are both constant terms with a value of 3, albeit with different signs. Like terms with constant terms can be combined by adding or subtracting their coefficients to simplify expressions and perform arithmetic operations.