Multiply :
`(ab - 1)(3-2ab)`

Answer

To solve the problem of multiplying the expressions \((ab - 1)(3 - 2ab)\), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Distribute each term in the first expression to each term in the second expression.

We will multiply each term in \((ab - 1)\) by each term in \((3 - 2ab)\):

\[ (ab - 1)(3 - 2ab) = ab \cdot 3 + ab \cdot (-2ab) - 1 \cdot 3 - 1 \cdot (-2ab) \]

### Step 2: Perform the multiplications.

Now we will calculate each of these products:

1. \(ab \cdot 3 = 3ab\)
2. \(ab \cdot (-2ab) = -2a^2b^2\)
3. \(-1 \cdot 3 = -3\)
4. \(-1 \cdot (-2ab) = +2ab\)

Putting these together, we have:

\[ 3ab - 2a^2b^2 - 3 + 2ab \]

### Step 3: Combine like terms.

Now we will combine the like terms \(3ab\) and \(2ab\):

\[ (3ab + 2ab) - 2a^2b^2 - 3 = 5ab - 2a^2b^2 - 3 \]

### Final Answer:

Thus, the final result of multiplying \((ab - 1)(3 - 2ab)\) is:

\[ 5ab - 2a^2b^2 - 3 \]

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