Find the value of ? ?.`(1008)^(2)` = ?

Answer

To find the value of \( (1008)^2 \), we can use the formula for the square of a binomial:

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

In this case, we can break down \( 1008 \) into \( 1000 + 8 \).

### Step 1: Identify \( a \) and \( b \)
Let:
- \( a = 1000 \)
- \( b = 8 \)

### Step 2: Apply the formula
Using the formula, we can calculate:

\[ (1000 + 8)^2 = 1000^2 + 2 \times 1000 \times 8 + 8^2 \]

### Step 3: Calculate each term
1. Calculate \( 1000^2 \):
\[ 1000^2 = 1000000 \]

2. Calculate \( 2 \times 1000 \times 8 \):
\[ 2 \times 1000 \times 8 = 16000 \]

3. Calculate \( 8^2 \):
\[ 8^2 = 64 \]

### Step 4: Sum all the terms
Now, we add all the calculated values together:

\[ 1000000 + 16000 + 64 \]

Calculating this step-by-step:

1. First, add \( 1000000 + 16000 \):
\[ 1000000 + 16000 = 1016000 \]

2. Then, add \( 64 \):
\[ 1016000 + 64 = 1016064 \]

### Final Answer
Thus, the value of \( (1008)^2 \) is:

\[ \boxed{1016064} \]