If a = 3, b = 2 and c = -4, find the values of:
`3ab-3b^(2)+4abc`

Answer

To find the value of the expression \(3ab - 3b^2 + 4abc\) given \(a = 3\), \(b = 2\), and \(c = -4\), we will follow these steps:

### Step 1: Substitute the values of \(a\), \(b\), and \(c\) into the expression.
We have:
- \(a = 3\)
- \(b = 2\)
- \(c = -4\)

Substituting these values into the expression:
\[ 3(3)(2) - 3(2^2) + 4(3)(2)(-4) \]

### Step 2: Calculate each term separately.
1. Calculate \(3ab\):
\[ 3ab = 3 \times 3 \times 2 = 18 \]

2. Calculate \(-3b^2\):
\[ -3b^2 = -3 \times (2^2) = -3 \times 4 = -12 \]

3. Calculate \(4abc\):
\[ 4abc = 4 \times 3 \times 2 \times (-4) = 4 \times 3 \times 2 \times -4 \]
First, calculate \(4 \times 3 = 12\), then \(12 \times 2 = 24\), and finally \(24 \times -4 = -96\).

### Step 3: Combine all the terms.
Now, we combine the results from the previous calculations:
\[ 18 - 12 - 96 \]

### Step 4: Simplify the expression.
1. First, simplify \(18 - 12\):
\[ 18 - 12 = 6 \]

2. Now, subtract \(96\):
\[ 6 - 96 = -90 \]

### Final Answer:
The value of the expression \(3ab - 3b^2 + 4abc\) is \(-90\).

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