The value of `(1001)^(3)` is.
`(1001)^(3)` का मान क्या है?

Options

A. `103003001`
B. `1003003001`
C. `100303001`
D. `100300301`

Explanation

To find the value of \( (1001)^3 \), we can use the binomial expansion formula for \( (a + b)^3 \), which is given by:

\[ (a + b)^3 = a^3 + b^3 + 3ab(a + b) \]

In this case, we can set \( a = 1000 \) and \( b = 1 \). Therefore, we can rewrite \( (1001)^3 \) as:

\[ (1001)^3 = (1000 + 1)^3 \]

Now, applying the binomial expansion:

1. **Calculate \( a^3 \)**:
\[ a^3 = (1000)^3 = 1000 \times 1000 \times 1000 = 1000000000 \]

2. **Calculate \( b^3 \)**:
\[ b^3 = (1)^3 = 1 \]

3. **Calculate \( 3ab(a + b) \)**:
\[ 3ab(a + b) = 3 \times 1000 \times 1 \times (1000 + 1) = 3 \times 1000 \times 1 \times 1001 \]
First, calculate \( 3 \times 1000 = 3000 \).
Then, calculate \( 3000 \times 1001 = 3003000 \).

4. **Combine all parts together**:
\[ (1001)^3 = a^3 + b^3 + 3ab(a + b) = 1000000000 + 1 + 3003000 \]

5. **Perform the addition**:
\[ 1000000000 + 1 = 1000000001 \]
\[ 1000000001 + 3003000 = 1003003001 \]

Thus, the value of \( (1001)^3 \) is:

\[ \boxed{1003003001} \]