Evaluate: 397 × 397 + 104 × 104 + 2 × 397 × 104

Given data

• Expression: a² + b² + 2ab with a = 397, b = 104

Concept / Approach

• Use (a + b)² = a² + 2ab + b².

Step-by-step calculation

a + b = 397 + 104 = 501Value = (a + b)² = 501²501² = (500 + 1)² = 500² + 2 × 500 × 1 + 1 = 250000 + 1000 + 1 = 251001

Verification

Direct multiplication yields the same result; the identity avoids heavy arithmetic.

Final Answer

251001