Evaluate the square: 1397 × 1397.

Problem Restatement

Calculate 1397² quickly without full long multiplication.

Concept / Approach

Use the identity (a − b)² = a² − 2ab + b² with a = 1400 and b = 3.

Step-by-Step Calculation

1397 = 1400 − 3(1400 − 3)² = 1400² − 2 × 1400 × 3 + 3²= 1,960,000 − 8,400 + 9 = 1,951,609

Verification

Sanity check: 1400² = 1,960,000; the square should be slightly less — difference 8,391, consistent.

Final Answer

1951609