Evaluate: (768^3 + 232^3) ÷ (768^2 − 768×232 + 232^2)

Given data

• Compute (a^3 + b^3) / (a^2 − ab + b^2) with a = 768, b = 232.

Concept / Approach

• Identity: a^3 + b^3 = (a + b)(a^2 − ab + b^2).

Step-by-step calculation

(768^3 + 232^3) ÷ (768^2 − 768×232 + 232^2)= (768 + 232) = 1000

Verification

Substituting a and b into the identity shows exact cancellation.

Common pitfalls

• Trying to expand cubes numerically instead of using the factorization identity.

Final Answer

1000