Expand : (ii) `(3a - (1)/( a) )^2`

Answer

To expand the expression \((3a - \frac{1}{a})^2\), we will use the identity for the square of a binomial, which states that:

\[ (a - b)^2 = a^2 - 2ab + b^2 \]

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
In our case, let \(a = 3a\) and \(b = \frac{1}{a}\).

2. **Apply the formula**:
Using the formula, we can expand the expression:
\[ (3a - \frac{1}{a})^2 = (3a)^2 - 2(3a)(\frac{1}{a}) + \left(\frac{1}{a}\right)^2 \]

3. **Calculate each term**:
- Calculate \((3a)^2\):
\[ (3a)^2 = 9a^2 \]
- Calculate \(-2(3a)(\frac{1}{a})\):
\[ -2(3a)(\frac{1}{a}) = -6 \]
- Calculate \(\left(\frac{1}{a}\right)^2\):
\[ \left(\frac{1}{a}\right)^2 = \frac{1}{a^2} \]

4. **Combine all the terms**:
Now, we combine all the calculated terms:
\[ 9a^2 - 6 + \frac{1}{a^2} \]

5. **Final expression**:
The expanded form of \((3a - \frac{1}{a})^2\) is:
\[ 9a^2 - 6 + \frac{1}{a^2} \]

### Final Answer:
\[ (3a - \frac{1}{a})^2 = 9a^2 - 6 + \frac{1}{a^2} \]