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.
 

Learning about like and unlike terms helps make algebra easier to understand. These simple tips and tricks will help students quickly identify, group, and simplify terms while solving math problems.
 

• When identifying like terms, always check the letters and their powers, not the numbers.
  
   
• Terms are “like” only if both the variable(s) and their exponents match exactly.
  
   
• If the variable part changes (like a and b), they are unlike terms.
  
   
• You can add or subtract like terms but never unlike ones.
  
   
• When combining terms, remember to include the positive or negative sign before each term.

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: When creating a monthly budget, expenses like rent, groceries, and travel are unlike terms because they represent different categories. But if your child has several grocery bills, those can be added together as like terms since they belong to the same category.
  
   
• Construction and Architecture: Workers use like and unlike terms to stay organized. For example, in construction, cement bags of the same type can be counted together just like combining like terms. Materials that are different can’t be grouped together, as they are unlike terms. This helps workers plan better and avoid mistakes during construction.
   
• Classroom Seating or Grouping: In a classroom, students in the same team are grouped together, like combining like terms. Students from different teams stay separate, just like unlike terms, helping organize seating easily
   
• Distance or Travel Planning: When planning a trip, distances in the same units and along the same route can be added easily, like combining like terms. Distances in different units are unlike terms and can’t be added directly.
  
   
• Inventory or Stock Counting (Like Terms): In shops, similar items are grouped together, like combining like terms in math. Items of the same type, such as pens, can be added easily, while different ones, like pens and pencils, are counted separately.