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!