Factorise:
`9a (3a-5b) - 12 a ^(2) (3a - 5b )`

Answer

To factorise the expression \( 9a(3a - 5b) - 12a^2(3a - 5b) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Common Factor**:
The expression consists of two terms: \( 9a(3a - 5b) \) and \( -12a^2(3a - 5b) \). Both terms share a common factor of \( (3a - 5b) \).

2. **Factor Out the Common Factor**:
We can factor out \( (3a - 5b) \) from both terms:
\[ (3a - 5b)(9a - 12a^2) \]

3. **Simplify the Remaining Expression**:
Now, we need to simplify the expression \( 9a - 12a^2 \). We can factor out \( 3a \) from this expression:
\[ 9a - 12a^2 = 3a(3 - 4a) \]

4. **Combine the Factors**:
Substituting back, we get:
\[ (3a - 5b)(3a(3 - 4a)) \]

5. **Final Factorised Form**:
Therefore, the fully factorised form of the original expression is:
\[ 3a(3 - 4a)(3a - 5b) \]

### Final Answer:
\[ 3a(3 - 4a)(3a - 5b) \]