What is the value of `(1004)^(2) - (998)^(2)` ?

Options

A. 11012
B. 12012
C. 120012
D. 1212

Answer

To solve the expression \( (1004)^2 - (998)^2 \), we can use the difference of squares formula, which states that:

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

In our case, let \( a = 1004 \) and \( b = 998 \).

### Step 1: Identify \( a \) and \( b \)
We have:
- \( a = 1004 \)
- \( b = 998 \)

### Step 2: Calculate \( a - b \)
Now, we calculate \( a - b \):
\[ a - b = 1004 - 998 = 6 \]

### Step 3: Calculate \( a + b \)
Next, we calculate \( a + b \):
\[ a + b = 1004 + 998 = 2002 \]

### Step 4: Apply the difference of squares formula
Now we can substitute these values into the difference of squares formula:
\[ (1004)^2 - (998)^2 = (1004 - 998)(1004 + 998) = (6)(2002) \]

### Step 5: Calculate the final result
Now, we multiply the two results:
\[ 6 \times 2002 = 12012 \]

Thus, the value of \( (1004)^2 - (998)^2 \) is \( 12012 \).

### Final Answer
\[ \text{The value is } 12012. \]

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