Factorise :
`a(3a - 2)-1`

Answer

To factorise the expression \( a(3a - 2) - 1 \), we will follow these steps:

### Step 1: Expand the expression
First, we will distribute \( a \) into the bracket:
\[ a(3a - 2) - 1 = 3a^2 - 2a - 1 \]

### Step 2: Rearrange the expression
Next, we will rearrange the expression to make it easier to factor:
\[ 3a^2 - 2a - 1 = 3a^2 - 3a + a - 1 \]

### Step 3: Group the terms
Now, we will group the terms into two pairs:
\[ (3a^2 - 3a) + (a - 1) \]

### Step 4: Factor out common terms from each group
From the first group \( (3a^2 - 3a) \), we can factor out \( 3a \):
\[ 3a(a - 1) + 1(a - 1) \]

### Step 5: Factor out the common binomial factor
Now we can see that \( (a - 1) \) is a common factor:
\[ (3a + 1)(a - 1) \]

### Final Answer
Thus, the factorised form of the expression \( a(3a - 2) - 1 \) is:
\[ (3a + 1)(a - 1) \]

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