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

Answer

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

### Step 1: Rearrange the expression
First, we rearrange the expression to group the terms in a standard form:
\[ 3a^2 - 2a - 1 \]

### Step 2: Identify coefficients
In the expression \(3a^2 - 2a - 1\), we identify:
- Coefficient of \(a^2\) (first term) = 3
- Coefficient of \(a\) (middle term) = -2
- Constant term (last term) = -1

### Step 3: Split the middle term
We need to split the middle term \(-2a\) into two terms such that their product equals the product of the coefficient of \(a^2\) and the constant term. That is:
\[ 3 \times (-1) = -3 \]
We need two numbers that multiply to \(-3\) and add up to \(-2\). The numbers are \(-3\) and \(1\).

So we can rewrite the expression as:
\[ 3a^2 - 3a + 1a - 1 \]

### Step 4: Group the terms
Now, we group the terms:
\[ (3a^2 - 3a) + (1a - 1) \]

### Step 5: Factor out the common terms
From the first group \(3a^2 - 3a\), we can factor out \(3a\):
\[ 3a(a - 1) \]
From the second group \(1a - 1\), we can factor out \(1\):
\[ 1(a - 1) \]

### Step 6: Combine the factors
Now we can write the expression as:
\[ 3a(a - 1) + 1(a - 1) \]
We can factor out the common term \((a - 1)\):
\[ (a - 1)(3a + 1) \]

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

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