Evaluate :
`(i) (98)^(3) " " (ii) (598)^(3) " " (iii) (1003)^(3)`

Answer

To evaluate the cubes of the numbers given in the question, we will use the identities for the cube of a binomial.

### Step-by-Step Solution:

**(i) Evaluate \( (98)^3 \)**

1. **Rewrite 98 as a binomial**:
\[ 98 = 100 - 2 \]
Thus, we can express \( (98)^3 \) as:
\[ (98)^3 = (100 - 2)^3 \]

2. **Apply the identity for \( (a - b)^3 \)**:
The formula is:
\[ (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \]
Here, \( a = 100 \) and \( b = 2 \):
\[ (100 - 2)^3 = 100^3 - 3 \cdot 100^2 \cdot 2 + 3 \cdot 100 \cdot 2^2 - 2^3 \]

3. **Calculate each term**:
- \( 100^3 = 1000000 \)
- \( 3 \cdot 100^2 \cdot 2 = 3 \cdot 10000 \cdot 2 = 60000 \)
- \( 3 \cdot 100 \cdot 2^2 = 3 \cdot 100 \cdot 4 = 1200 \)
- \( 2^3 = 8 \)

4. **Combine the results**:
\[ (98)^3 = 1000000 - 60000 + 1200 - 8 \]
\[ = 1000000 - 60000 = 940000 \]
\[ = 940000 + 1200 = 941200 \]
\[ = 941200 - 8 = 941192 \]

**Final Result for (i)**:
\[ (98)^3 = 941192 \]

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**(ii) Evaluate \( (598)^3 \)**

1. **Rewrite 598 as a binomial**:
\[ 598 = 600 - 2 \]
Thus, we can express \( (598)^3 \) as:
\[ (598)^3 = (600 - 2)^3 \]

2. **Apply the identity for \( (a - b)^3 \)**:
Here, \( a = 600 \) and \( b = 2 \):
\[ (600 - 2)^3 = 600^3 - 3 \cdot 600^2 \cdot 2 + 3 \cdot 600 \cdot 2^2 - 2^3 \]

3. **Calculate each term**:
- \( 600^3 = 216000000 \)
- \( 3 \cdot 600^2 \cdot 2 = 3 \cdot 360000 \cdot 2 = 2160000 \)
- \( 3 \cdot 600 \cdot 2^2 = 3 \cdot 600 \cdot 4 = 7200 \)
- \( 2^3 = 8 \)

4. **Combine the results**:
\[ (598)^3 = 216000000 - 2160000 + 7200 - 8 \]
\[ = 216000000 - 2160000 = 213840000 \]
\[ = 213840000 + 7200 = 213847200 \]
\[ = 213847200 - 8 = 213847192 \]

**Final Result for (ii)**:
\[ (598)^3 = 213847192 \]

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**(iii) Evaluate \( (1003)^3 \)**

1. **Rewrite 1003 as a binomial**:
\[ 1003 = 1000 + 3 \]
Thus, we can express \( (1003)^3 \) as:
\[ (1003)^3 = (1000 + 3)^3 \]

2. **Apply the identity for \( (a + b)^3 \)**:
Here, \( a = 1000 \) and \( b = 3 \):
\[ (1000 + 3)^3 = 1000^3 + 3 \cdot 1000^2 \cdot 3 + 3 \cdot 1000 \cdot 3^2 + 3^3 \]

3. **Calculate each term**:
- \( 1000^3 = 1000000000 \)
- \( 3 \cdot 1000^2 \cdot 3 = 3 \cdot 1000000 \cdot 3 = 9000000 \)
- \( 3 \cdot 1000 \cdot 3^2 = 3 \cdot 1000 \cdot 9 = 27000 \)
- \( 3^3 = 27 \)

4. **Combine the results**:
\[ (1003)^3 = 1000000000 + 9000000 + 27000 + 27 \]
\[ = 1000000000 + 9000000 = 1009000000 \]
\[ = 1009000000 + 27000 = 1009027000 \]
\[ = 1009027000 + 27 = 1009027027 \]

**Final Result for (iii)**:
\[ (1003)^3 = 1009027027 \]

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### Summary of Results:
1. \( (98)^3 = 941192 \)
2. \( (598)^3 = 213847192 \)
3. \( (1003)^3 = 1009027027 \)