`(998)^(2)`

Answer

To solve the expression \( (998)^2 \), we can use the formula for the square of a binomial, which is given by:

\[ (a - b)^2 = a^2 - 2ab + b^2 \]

In this case, we can express \( 998 \) as \( 1000 - 2 \). So, we can rewrite the expression as:

\[ (998)^2 = (1000 - 2)^2 \]

Now, we can apply the binomial square formula:

1. **Identify \( a \) and \( b \)**:
- Here, \( a = 1000 \) and \( b = 2 \).

2. **Apply the formula**:
\[ (1000 - 2)^2 = 1000^2 - 2 \cdot 1000 \cdot 2 + 2^2 \]

3. **Calculate each term**:
- \( 1000^2 = 1000000 \)
- \( 2 \cdot 1000 \cdot 2 = 8000 \)
- \( 2^2 = 4 \)

4. **Substitute back into the equation**:
\[ (1000 - 2)^2 = 1000000 - 8000 + 4 \]

5. **Perform the arithmetic**:
- First, subtract \( 8000 \) from \( 1000000 \):
\[ 1000000 - 8000 = 992000 \]
- Then, add \( 4 \):
\[ 992000 + 4 = 992004 \]

Thus, the final result is:

\[ (998)^2 = 992004 \]