Find the square of:
`(3a)/(2b) - (2b)/(3a)`

Answer

To find the square of the expression \(\frac{3a}{2b} - \frac{2b}{3a}\), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ \left(\frac{3a}{2b} - \frac{2b}{3a}\right)^2 \]

### Step 2: Use the square of a binomial formula
We will use the formula for the square of a binomial:
\[ (x - y)^2 = x^2 + y^2 - 2xy \]
In our case, let:
\[ x = \frac{3a}{2b} \quad \text{and} \quad y = \frac{2b}{3a} \]
So, we can rewrite the expression as:
\[ \left(\frac{3a}{2b}\right)^2 + \left(\frac{2b}{3a}\right)^2 - 2\left(\frac{3a}{2b}\right)\left(\frac{2b}{3a}\right) \]

### Step 3: Calculate \(x^2\)
Now, we calculate \(x^2\):
\[ \left(\frac{3a}{2b}\right)^2 = \frac{(3a)^2}{(2b)^2} = \frac{9a^2}{4b^2} \]

### Step 4: Calculate \(y^2\)
Next, we calculate \(y^2\):
\[ \left(\frac{2b}{3a}\right)^2 = \frac{(2b)^2}{(3a)^2} = \frac{4b^2}{9a^2} \]

### Step 5: Calculate \(2xy\)
Now, we calculate \(2xy\):
\[ 2\left(\frac{3a}{2b}\right)\left(\frac{2b}{3a}\right) = 2 \cdot \frac{3a \cdot 2b}{2b \cdot 3a} = 2 \cdot 1 = 2 \]

### Step 6: Combine all parts
Now, we can combine all the parts together:
\[ \frac{9a^2}{4b^2} + \frac{4b^2}{9a^2} - 2 \]

### Final Result
Thus, the square of the expression \(\frac{3a}{2b} - \frac{2b}{3a}\) is:
\[ \frac{9a^2}{4b^2} + \frac{4b^2}{9a^2} - 2 \]

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