Using suitable identity, evaluate:
`(97)^(3)`

Answer

To evaluate \( 97^3 \) using a suitable identity, we can express \( 97 \) as \( 100 - 3 \). We will then use the binomial expansion formula for \( (x - y)^3 \).

### Step-by-Step Solution:

1. **Rewrite the expression**:
\[ 97^3 = (100 - 3)^3 \]

2. **Apply the binomial expansion formula**:
The formula for \( (x - y)^3 \) is given by:
\[ x^3 - 3x^2y + 3xy^2 - y^3 \]
Here, \( x = 100 \) and \( y = 3 \).

3. **Substituting the values into the formula**:
\[ (100 - 3)^3 = 100^3 - 3 \cdot 100^2 \cdot 3 + 3 \cdot 100 \cdot 3^2 - 3^3 \]

4. **Calculate each term**:
- \( 100^3 = 1000000 \)
- \( 3 \cdot 100^2 \cdot 3 = 3 \cdot 10000 \cdot 3 = 90000 \)
- \( 3 \cdot 100 \cdot 3^2 = 3 \cdot 100 \cdot 9 = 2700 \)
- \( 3^3 = 27 \)

5. **Combine the terms**:
\[ 97^3 = 1000000 - 90000 + 2700 - 27 \]

6. **Perform the calculations step-by-step**:
- First, calculate \( 1000000 - 90000 = 910000 \)
- Then, \( 910000 + 2700 = 912700 \)
- Finally, \( 912700 - 27 = 912673 \)

Thus, the value of \( 97^3 \) is:
\[ \boxed{912673} \]