If (a^{3}+b^{3}) is proportional to (a^{2}-b^{2}), then (a^{2}-ab+b^{2}) is proportional to
- A. (a-b) ✓
- B. (a+b)
- C. (a+ab+b)
- D. (a^{3}-b^{3})
Correct Answer: A. (a-b)
Explanation
Given \frac{a^3+b^3}{a^2-b^2} = k. Using algebraic identities, \frac{(a+b)(a^2-ab+b^2)}{(a-b)(a+b)} = k \implies \frac{a^2-ab+b^2}{a-b} = k. Thus, (a^2-ab+b^2) is proportional to (a-b).
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