Evaluate (489 + 375)^2 − (489 − 375)^2.

Given data

• Compute (x + y)^2 − (x − y)^2 for x = 489, y = 375.

Concept / Approach

• Identity: (x + y)^2 − (x − y)^2 = 4xy (difference of squares of conjugates).

Step-by-step calculation

x·y = 489 × 375 = (500 − 11) × 375 = 187,500 − 4,125 = 183,3754xy = 4 × 183,375 = 733,500

Verification

(489 + 375) = 864, (489 − 375) = 114; 864^2 − 114^2 = (864 − 114)(864 + 114) = 750 × 978 = 733,500.

Final Answer

733500