If ` a = 4.965 , b = 2.343 and c = 2. 622 `, then the value of ` a^(3) - b^(3) - c^(3) - 3abc ` is

Options

A. `-2`
B. `-1`
C. 0
D. `9 . 0 ^(3)`

Answer

To solve the problem, we need to calculate the expression \( a^3 - b^3 - c^3 - 3abc \) using the given values of \( a \), \( b \), and \( c \).

### Step-by-Step Solution:

1. **Identify the values:**
- \( a = 4.965 \)
- \( b = 2.343 \)
- \( c = 2.622 \)

2. **Calculate \( a^3 \):**
\[ a^3 = (4.965)^3 \]
Calculating \( 4.965^3 \):
\[ a^3 \approx 122.095 \]

3. **Calculate \( b^3 \):**
\[ b^3 = (2.343)^3 \]
Calculating \( 2.343^3 \):
\[ b^3 \approx 12.910 \]

4. **Calculate \( c^3 \):**
\[ c^3 = (2.622)^3 \]
Calculating \( 2.622^3 \):
\[ c^3 \approx 18.028 \]

5. **Calculate \( 3abc \):**
\[ 3abc = 3 \times (4.965) \times (2.343) \times (2.622) \]
First, calculate \( abc \):
\[ abc \approx 4.965 \times 2.343 \times 2.622 \approx 29.032 \]
Now, multiply by 3:
\[ 3abc \approx 3 \times 29.032 \approx 87.096 \]

6. **Combine all parts to find \( a^3 - b^3 - c^3 - 3abc \):**
\[ a^3 - b^3 - c^3 - 3abc \approx 122.095 - 12.910 - 18.028 - 87.096 \]
Now, calculate:
\[ 122.095 - 12.910 \approx 109.185 \]
\[ 109.185 - 18.028 \approx 91.157 \]
\[ 91.157 - 87.096 \approx 4.061 \]

### Final Answer:
The value of \( a^3 - b^3 - c^3 - 3abc \) is approximately \( 4.061 \).

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