What Is the Difference Between Like and Unlike 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

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.