We are tasked with factorizing the expression \( 18e^3f - 12e^3f \).

### Step-by-step solution:

1. **Factor out the common term**:  
   The terms \( 18e^3f \) and \( 12e^3f \) both have the common factor \( e^3f \). So, we factor that out:

   \[
   18e^3f - 12e^3f = e^3f(18 - 12)
   \]

2. **Simplify inside the parentheses**:  
   Subtract the constants inside the parentheses:

   \[
   18 - 12 = 6
   \]

3. **Final factored form**:  
   After simplifying, the expression becomes:

   \[
   e^3f(6)
   \]

   or simply:

   \[
   6e^3f
   \]

Thus, the fully factored form of \( 18e^3f - 12e^3f \) is \( 6e^3f \).

Would you like more details or explanations on any part of the solution?

### Relative Questions:
1. How do you factor out the greatest common factor from more complex terms?
2. Can factorization involve non-numeric coefficients like functions?
3. What are some common factorization techniques?
4. How does factorization help in solving algebraic equations?
5. What is the difference between factoring and expanding an expression?

**Tip:** Always look for common factors first when starting to factorize an expression.

Learn how to factorize the expression 18e^3f - 12e^3f fully using the greatest common factor (GCF). This problem focuses on algebraic factoring techniques, including the distributive property. Suitable for students in Grades 8-10.

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