Simplify Expression: Definition And Examples

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. 

Example: 

Simplify 3x + 2(x – 4) 

Solution: 

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. 

Hence,  

  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. 

Coefficient:  

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.  

Solution: 

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). 

Solution: 

8n+12+(- 9) -(-6n) 

Combine the numeric terms: 

14n+12-9 

14n+3 

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 

Solution: 

2/5m -4/5 – 3/5 m 

Example 2: 

Simplify the expression 

-4/7p + ( -2/7p) + 1/7

Solution: 

-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 

=4b+11c. 

Example 1: 

Simplify the expression 9x +3y-2x+5. 

Solution: 

9x +3y-2x+5 +2y 

Example2: 

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

Solution: 

9y+3-4x-2y-3x-5 

Exercise:

1. Simplify the expression:
   -3+3v+(-4v)
2. Simplify the expression:
   –6b+9b–5b
3. Combine like terms.
   2x+4x—5y+3
4. Simplify the expression:
   -5.8c+4.2-3.1+1.4c−5.8c+4.2−3.1+1.4c
5. Combine like terms.
   7x + 6y + 6x
6. Combine like terms with two variables.
   5t+7p-4p—2t
7. Combine like terms with two variables.
   4.7+5g+4k+11.1-2g
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.