Need Help?

Get in touch with us


Simplify Expression: Definition And Examples

Grade 7
Sep 17, 2022

Key Concepts

  • Combine like terms with integer coefficients
  • Combine like terms with rational coefficients
  • Combine like terms with two variables

4.3 Simplify expressions 

To simplify any algebraic expression, the following are the basic rules and steps: 

  • Remove any grouping symbol such as brackets and parentheses by multiplying factors.  
  • Use the exponent rule to remove grouping if the terms contain exponents.  
  • Combine the like terms by addition or subtraction. 
  • Combine the constants. 


Simplify 3x + 2(x – 4) 


3x + 2(x – 4) 


In this case, it is impossible to combine terms when they are still in parentheses or any grouping sign.  

Therefore, eliminate the parenthesis by multiplying any factor outside the grouping by all terms inside it. 


  3x + 2(x – 4)  

= 3x + 2x – 8  


= 5x – 8 

4.3.1 Combine like terms with integer coefficients 

Like terms:  

In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. 


A coefficient is a number multiplied by a variable. 

Integer coefficient: 

In mathematics, an integer-valued polynomial (also known as a numerical polynomial) is a polynomial whose value is an integer for every integer n.  

Every polynomial with integer coefficients is integer-valued, but the converse is not true. 

Example 1: 

Simplify the expression – 3c+5c—4 -4c+6.  


Write the expression by grouping like terms together. 

Step 2: Combine like terms. 

(-3c-4c+5c) +(-4+6) 

– 2c+2 

Example 2: 

Simplify the expression 8n+12+(- 9) -(-6n). 


8n+12+(- 9) -(-6n) 

Combine the numeric terms: 



The simplified expression is 14n+3. 

4.3.2 Combine like terms with rational coefficients  

Example 1: 

Simplify the expression 

2/5m – 4/5 – 3/5 m 


2/5m -4/5 – 3/5 m 

Example 2: 

Simplify the expression 

-4/7p + ( -2/7p) + 1/7


-4/7p + ( -2/7 p) + 1/7

4.3.3 Combine like terms with two variables 

Here b and c are the two variables. 

6b and -2b are the like terms. 

4c and 7c are the like terms. 

Combine like terms 


Example 1: 

Simplify the expression 9x +3y-2x+5. 


9x +3y-2x+5 +2y 


Simplify the expression 9y+3-4x-2y-3x-5 




  1. Simplify the expression:
  2. Simplify the expression:
  3. Combine like terms.
  4. Simplify the expression:
  5. Combine like terms.
    7x + 6y + 6x
  6. Combine like terms with two variables.
  7. Combine like terms with two variables.
  8. Simplify -8+(⅓y) +5-(⁴⁄₃y)
  9. Which expression is equivalent to 8k+9k?

10. Which expression is equivalent to c+c+r+r+r?

Concept Map

What have we learned:

  • Identify like terms.
  • Understand how to combine like terms with integer coefficients.
  • Understand how to combine like terms with rational coefficients.
  • Combine like terms with two variables.


Related topics

Addition and Multiplication Using Counters and Bar-Diagrams

Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]


Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Numerical Expressions

How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division  A → Addition S → Subtraction         Some examples […]

System of linear inequalities

System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]


Other topics