Find the products
`[-4ab]xx[-3a^(2)bc]`

Options

A. `-12a^3b^3c`
B. `12a^3b^3c`
C. `12a^3b^2c`
D. `-12a^3b^2c`

Answer

To find the product of the expressions \([-4ab]\) and \([-3a^2bc]\), we will follow these steps:

### Step 1: Multiply the coefficients
We start by multiplying the coefficients (the numerical parts) of the two expressions. The coefficients are \(-4\) and \(-3\).

\[ -4 \times -3 = 12 \]

### Step 2: Multiply the variables
Next, we will multiply the variable parts. We have \(ab\) from the first expression and \(a^2bc\) from the second expression.

1. **Multiply the \(a\) terms**:
- We have \(a^1\) from \(-4ab\) and \(a^2\) from \(-3a^2bc\).
- When multiplying \(a^1\) and \(a^2\), we add the exponents:
\[ a^1 \times a^2 = a^{1+2} = a^3 \]

2. **Multiply the \(b\) terms**:
- We have \(b^1\) from \(-4ab\) and \(b^1\) from \(-3a^2bc\).
- When multiplying \(b^1\) and \(b^1\), we add the exponents:
\[ b^1 \times b^1 = b^{1+1} = b^2 \]

3. **Include the \(c\) term**:
- The second expression has \(c^1\) (since \(c\) is not present in the first expression, we consider it as \(c^1\)).
- Therefore, we keep \(c\) as it is.

### Step 3: Combine all parts
Now we combine the results from the coefficients and the variables:

\[ 12 \times a^3 \times b^2 \times c = 12a^3b^2c \]

### Final Answer
The product of the expressions \([-4ab]\) and \([-3a^2bc]\) is:

\[ \boxed{12a^3b^2c} \]