`(197 xx 203) = ?`

Options

A. 39991
B. 39999
C. 40009
D. 40001

Answer

To solve the problem \( 197 \times 203 \), we can use the identity for the difference of squares, which states that:

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

### Step-by-Step Solution:

1. **Rewrite the Numbers**:
We can express \( 197 \) and \( 203 \) in terms of \( 200 \):
\[ 197 = 200 - 3 \quad \text{and} \quad 203 = 200 + 3 \]

2. **Apply the Identity**:
Now, we can use the difference of squares identity:
\[ (200 - 3)(200 + 3) = 200^2 - 3^2 \]

3. **Calculate \( 200^2 \)**:
\[ 200^2 = 40000 \]

4. **Calculate \( 3^2 \)**:
\[ 3^2 = 9 \]

5. **Subtract the Squares**:
Now, substitute these values back into the equation:
\[ 200^2 - 3^2 = 40000 - 9 \]

6. **Perform the Subtraction**:
\[ 40000 - 9 = 39991 \]

Thus, the final answer is:
\[ \boxed{39991} \]