Use identities to evaluate: `(998)^(2)`

Answer

To evaluate \( (998)^2 \) using identities, we can follow these steps:

### Step-by-Step Solution

1. **Rewrite the expression**:
\[ (998)^2 = (1000 - 2)^2 \]

2. **Apply the identity**:
We will use the identity \( (x - y)^2 = x^2 - 2xy + y^2 \). Here, \( x = 1000 \) and \( y = 2 \).
\[ (1000 - 2)^2 = 1000^2 - 2 \cdot 1000 \cdot 2 + 2^2 \]

3. **Calculate each term**:
- Calculate \( 1000^2 \):
\[ 1000^2 = 1000000 \]
- Calculate \( 2^2 \):
\[ 2^2 = 4 \]
- Calculate \( 2 \cdot 1000 \cdot 2 \):
\[ 2 \cdot 1000 \cdot 2 = 4000 \]

4. **Substitute back into the equation**:
\[ (1000 - 2)^2 = 1000000 - 4000 + 4 \]

5. **Combine the terms**:
\[ 1000000 - 4000 = 996000 \]
\[ 996000 + 4 = 996004 \]

Thus, the value of \( (998)^2 \) is \( 996004 \).