Evaluate (963 + 476)^2 + (963 − 476)^2.

Given data

• Compute S = (a + b)^2 + (a − b)^2 for a = 963, b = 476.

Concept / Approach

• Identity: (a + b)^2 + (a − b)^2 = 2(a^2 + b^2)

Step-by-step calculation

a^2 = 963^2 = (1000 − 37)^2 = 1000000 − 74000 + 1369 = 927369b^2 = 476^2 = (500 − 24)^2 = 250000 − 24000 + 576 = 226576a^2 + b^2 = 927369 + 226576 = 1153945S = 2(a^2 + b^2) = 2 × 1153945 = 2307890

Alternative check

(963 + 476) = 1439, (963 − 476) = 487 ⇒ 1439^2 + 487^2 = 2(963^2 + 476^2) (same identity).

Common pitfalls

• Expanding both squares manually (time-consuming and error-prone).
• Forgetting the factor 2 in the identity result.

Final Answer

Value = 2307890.