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

Answer

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

### Step 1: Identify the common factor
We notice that both terms in the expression share a common factor of \( (a - 2b) \).

### Step 2: Rewrite the expression
We can express the original equation by factoring out the common term:
\[ 3(a - 2b)^2 - 5(a - 2b) = (a - 2b)(3(a - 2b) - 5) \]

### Step 3: Simplify the expression inside the parentheses
Now, we simplify the expression inside the parentheses:
\[ 3(a - 2b) - 5 \]

### Step 4: Write the final factored form
Putting it all together, we have:
\[ (a - 2b)(3(a - 2b) - 5) \]

### Step 5: Further simplify if necessary
We can leave it as is or simplify the second term further, but it is already in a good factored form:
\[ (a - 2b)(3a - 6b - 5) \]

Thus, the final factored form is:
\[ (a - 2b)(3a - 6b - 5) \]