Using suitable identity evaluate the
`(729) ^(2) - (271) ^(2)`

Options

A. 456000
B. 468000
C. 485000
D. 458000

Answer

To evaluate \( (729)^2 - (271)^2 \) using a suitable identity, we can use the identity for the difference of squares:

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

### Step-by-Step Solution:

1. **Identify \( a \) and \( b \)**:
Here, we can let:
- \( a = 729 \)
- \( b = 271 \)

2. **Apply the identity**:
Using the identity \( a^2 - b^2 = (a - b)(a + b) \), we can rewrite the expression:
\[ (729)^2 - (271)^2 = (729 - 271)(729 + 271) \]

3. **Calculate \( a - b \)**:
Now, we calculate \( 729 - 271 \):
\[ 729 - 271 = 458 \]

4. **Calculate \( a + b \)**:
Next, we calculate \( 729 + 271 \):
\[ 729 + 271 = 1000 \]

5. **Multiply the results**:
Now we can multiply the two results:
\[ (729)^2 - (271)^2 = 458 \times 1000 \]

6. **Final calculation**:
Finally, we calculate \( 458 \times 1000 \):
\[ 458 \times 1000 = 458000 \]

### Conclusion:
Thus, the value of \( (729)^2 - (271)^2 \) is \( 458000 \).

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