The algebraic identity that can be used in evaluating the value of `(98)^(2)` is __________.

Answer

To evaluate the value of \( (98)^2 \) using an algebraic identity, we can use the identity for the square of a binomial, specifically \( (a - b)^2 = a^2 - 2ab + b^2 \).

### Step-by-Step Solution:

1. **Identify the values of \( a \) and \( b \)**:
We can express \( 98 \) as \( 100 - 2 \). Here, we let:
- \( a = 100 \)
- \( b = 2 \)

2. **Apply the identity**:
Using the identity \( (a - b)^2 = a^2 - 2ab + b^2 \), we substitute \( a \) and \( b \):
\[ (100 - 2)^2 = 100^2 - 2 \cdot 100 \cdot 2 + 2^2 \]

3. **Calculate each term**:
- Calculate \( a^2 \):
\[ 100^2 = 10000 \]
- Calculate \( 2ab \):
\[ 2 \cdot 100 \cdot 2 = 400 \]
- Calculate \( b^2 \):
\[ 2^2 = 4 \]

4. **Combine the terms**:
Now, substitute these values back into the equation:
\[ (100 - 2)^2 = 10000 - 400 + 4 \]

5. **Perform the arithmetic**:
- First, combine \( 10000 \) and \( 4 \):
\[ 10000 + 4 = 10004 \]
- Then subtract \( 400 \):
\[ 10004 - 400 = 9604 \]

6. **Final result**:
Therefore, the value of \( (98)^2 \) is:
\[ 98^2 = 9604 \]