The value of `a^3 + b^3 + c^3 - 3abc`, when `a = 87, b = -126 and c = 39` is :

Options

A. 0
B. 1259
C. `-48`
D. None of these

Answer

To solve the expression \( a^3 + b^3 + c^3 - 3abc \) for the given values \( a = 87 \), \( b = -126 \), and \( c = 39 \), we can use the identity:

\[ a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc) \]

### Step-by-Step Solution:

1. **Calculate \( a + b + c \)**:
\[ a + b + c = 87 + (-126) + 39 \]
\[ = 87 - 126 + 39 \]
\[ = 126 - 126 = 0 \]

2. **Calculate \( a^2 + b^2 + c^2 \)**:
\[ a^2 = 87^2 = 7569 \]
\[ b^2 = (-126)^2 = 15876 \]
\[ c^2 = 39^2 = 1521 \]
\[ a^2 + b^2 + c^2 = 7569 + 15876 + 1521 \]
\[ = 24966 \]

3. **Calculate \( ab, ac, bc \)**:
\[ ab = 87 \times (-126) = -10962 \]
\[ ac = 87 \times 39 = 3393 \]
\[ bc = (-126) \times 39 = -4914 \]

4. **Calculate \( a^2 + b^2 + c^2 - ab - ac - bc \)**:
\[ a^2 + b^2 + c^2 - ab - ac - bc = 24966 - (-10962) - 3393 - (-4914) \]
\[ = 24966 + 10962 - 3393 + 4914 \]
\[ = 24966 + 10962 + 4914 - 3393 \]
\[ = 24966 + 10962 + 4914 - 3393 = 30549 \]

5. **Final Calculation**:
Since \( a + b + c = 0 \), we can conclude:
\[ a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc) = 0 \times 30549 = 0 \]

### Final Answer:
\[ \text{The value of } a^3 + b^3 + c^3 - 3abc \text{ is } 0. \]