Find the value of the following.
`abc - ab-bc` for a = 2, b= -3,c=-1

Options

A. 6
B. 7
C. 9
D. 8

Answer

To find the value of the expression \( abc - ab - bc \) for \( a = 2 \), \( b = -3 \), and \( c = -1 \), we will follow these steps:

### Step 1: Substitute the values of a, b, and c into the expression.
The expression is:
\[ abc - ab - bc \]
Substituting \( a = 2 \), \( b = -3 \), and \( c = -1 \):
\[ (2)(-3)(-1) - (2)(-3) - (-3)(-1) \]

### Step 2: Calculate \( abc \).
Calculating \( abc \):
\[ (2)(-3)(-1) = 2 \times -3 = -6 \quad \text{and then} \quad -6 \times -1 = 6 \]
So, \( abc = 6 \).

### Step 3: Calculate \( ab \).
Calculating \( ab \):
\[ (2)(-3) = -6 \]
So, \( ab = -6 \).

### Step 4: Calculate \( bc \).
Calculating \( bc \):
\[ (-3)(-1) = 3 \]
So, \( bc = 3 \).

### Step 5: Substitute the calculated values back into the expression.
Now we substitute \( abc = 6 \), \( ab = -6 \), and \( bc = 3 \) back into the expression:
\[ 6 - (-6) - 3 \]

### Step 6: Simplify the expression.
This simplifies to:
\[ 6 + 6 - 3 \]
Calculating this step-by-step:
1. \( 6 + 6 = 12 \)
2. \( 12 - 3 = 9 \)

### Final Answer:
Thus, the value of the expression \( abc - ab - bc \) is \( 9 \).

---