Evaluate using suitable identitiie.
`497 xx 505`

Answer

To evaluate \( 497 \times 505 \) using suitable identities, we can use the identity for the product of two numbers in the form of \( (a - b)(a + b) = a^2 - b^2 \).

### Step-by-Step Solution:

1. **Rewrite the Numbers**:
We can express \( 497 \) and \( 505 \) in terms of \( 500 \):
\[ 497 = 500 - 3 \quad \text{and} \quad 505 = 500 + 5 \]

2. **Apply the Identity**:
Now, we can use the identity:
\[ (a - b)(a + b) = a^2 - b^2 \]
Here, let \( a = 500 \), \( b = 3 \) and \( c = 5 \). We will calculate:
\[ 497 \times 505 = (500 - 3)(500 + 5) \]

3. **Expand the Expression**:
Using the distributive property:
\[ (500 - 3)(500 + 5) = 500 \times 500 + 500 \times 5 - 3 \times 500 - 3 \times 5 \]

4. **Calculate Each Term**:
- \( 500 \times 500 = 250000 \)
- \( 500 \times 5 = 2500 \)
- \( -3 \times 500 = -1500 \)
- \( -3 \times 5 = -15 \)

5. **Combine the Results**:
Now, we combine all these results:
\[ 250000 + 2500 - 1500 - 15 \]

6. **Perform the Addition and Subtraction**:
- First, add \( 250000 + 2500 = 252500 \)
- Then, subtract \( 1500 \): \( 252500 - 1500 = 251000 \)
- Finally, subtract \( 15 \): \( 251000 - 15 = 250985 \)

Thus, the final answer is:
\[ \boxed{250985} \]