Like and Unlike Algebraic Terms

Like terms are terms that have the same variables with the same exponents, but they can have different coefficients. For example:

3x2 and 5x2 are like terms because both have the variable x2.

2xy and −7xy are like terms because both have the variable xy.
 

Unlike terms are defined as terms with different variables, or the same variables with different exponents. For example:

4x and 4y are unlike terms because they have different variables.

3x2 and 3x are unlike terms because the terms have different exponents.

ab and a2b are unlike terms because they have different powers of a.

The variables and their powers decide whether two terms are like or unlike. Understanding the difference between them helps us simplify and solve algebraic expressions.
 

Like terms can be added or subtracted easily by following these simple steps:
Step 1: Identify like terms—these are terms that have the same variables with the same exponents. Once identified, you can add or subtract their coefficients. For example, 2x + 3x = 5x.
Step 2: Add or subtract the coefficients of like terms while keeping the variable unchanged. For example, 6y + 3y = (3 + 6) y = 9y.
Step 3: Keep the sign in mind, pay attention to the signs (+/−) of each term when adding or subtracting. 10y -15y = -5y.
 

Unlike, terms cannot be added or subtracted because they have different variables or different exponents, making them impossible to combine. Here’s how to handle them: 
Step 1: Do not combine unlike terms. Instead, leave them as they are. For example, 3x + 7y cannot be simplified, so it stays as it is. 
Step 2: Write them in a simplified and organized manner, without combining them.
 

Like and unlike terms aren’t just for solving equations in class, they also help us to solve practical, real-life problems. Here are some real-life applications of like and unlike algebraic terms.  

• Budgeting and Finances: Creating a monthly budget, expenses like rent, groceries, and travel are categorized under unlike terms as they represent different things (or variables). But repeated items like multiple grocery bills can be added together as like terms.
• Construction and Architecture: Workers use like and unlike terms to keep things organized. For example, In construction materials like cement bags of the same type can be counted together which is similar to combining terms. If the materials cannot be combined, they are unlike terms and must be kept separate. This helps to plan better and avoid mistakes in construction.
• Classroom Seating or Grouping: In a classroom, students who are in the same house or team are often grouped together. This is similar to combining like terms in algebra. This is similar to combining like terms in algebra. Students are from different groups, they are kept separate similar to unlike terms that cannot be combined. This helps in seating and organizing the class easily.
• Distance or Travel Planning: While planning a travel, the distances can be added easily when they are in the same units (either kms or miles) and follow the same route, just like adding like terms in math. But if the distances are given in different units of length, they cannot be added directly, similar to unlike terms. Using like terms in planning helps keep the total distance clear and organized.
• Inventory or Stock Counting (Like Terms): In shops or stores, similar items are put together, just like unlike terms in math. If the items are the same type, like pens, can be added easily. But different items, such as pens and pencils, are counted separately, just like unlike terms that cannot be combined. This helps in keeping the stock organized and accurate.