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Let's solve the given expression for Question 3 (i), which is:

**Factorise: \( 6abc - 9a^2c \)**

### Step-by-step solution:

1. **Identify the common factors**:
   - In the first term \( 6abc \), the factors are \( 6 \), \( a \), \( b \), and \( c \).
   - In the second term \( 9a^2c \), the factors are \( 9 \), \( a^2 \), and \( c \).

   The common factors between both terms are:
   - \( 3 \) (common divisor of \( 6 \) and \( 9 \)),
   - \( a \) (since both terms have at least one factor of \( a \)),
   - \( c \) (since both terms have \( c \)).

2. **Factor out the common factors**:
   The common factors are \( 3ac \). So, we factor \( 3ac \) out of both terms:

   \[
   6abc - 9a^2c = 3ac(2b - 3a)
   \]

### Final answer:
\[
6abc - 9a^2c = 3ac(2b - 3a)
\]

Would you like further explanation or have any questions?

Here are some related questions to deepen understanding:
1. How would you factor \( 12abc - 18a^2bc \)?
2. What would happen if the sign in the expression were different, e.g., \( 6abc + 9a^2c \)?
3. Can you factor \( 15a^2b - 20ab^2 \) in a similar way?
4. If \( c = 0 \), how would that affect the original expression \( 6abc - 9a^2c \)?
5. What is the greatest common factor between \( 6abc \) and \( 9a^2c \)?

**Tip**: Always look for the greatest common factor before attempting any further factorization steps!

Learn how to factorize the algebraic expression 6abc - 9a^2c by extracting the greatest common factor (GCF). Suitable for students in Grades 7-9, this problem involves basic algebra and factorization techniques.

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