Which value equals (α+β)^3?

Which value equals (α+β)^3?

• A. α^3 + β^3 + 3αβ(α+β)
• B. α^3 + β^3
• C. α^3 + β^3 + 6αβ(α+β)
• D. α^2β^2

Answer: (A)

Expanding a cube of a sum uses the binomial terms: (α+β)^3 = α^3 + 3α^2β + 3αβ^2 + β^3. The middle two terms factor as 3αβ(α+β), so the full expression becomes α^3 + β^3 + 3αβ(α+β). This matches the given form. The other options miss the cross terms, overcount them, or are not cubic in total.

Expanding a cube of a sum uses the binomial terms: (α+β)^3 = α^3 + 3α^2β + 3αβ^2 + β^3. The middle two terms factor as 3αβ(α+β), so the full expression becomes α^3 + β^3 + 3αβ(α+β). This matches the given form. The other options miss the cross terms, overcount them, or are not cubic in total.