Which expression equals (α+β+γ+δ)^2?

Which expression equals (α+β+γ+δ)^2?

• A. α^2+β^2+γ^2+δ^2
• B. (α+β+γ+δ)^2
• C. α^2+β^2+γ^2+δ^2 + 2(αβ+αγ+αδ+βγ+βδ+γδ)
• D. α^2+β^2+γ^2+δ^2 - 2(αβ+αγ+αδ+βγ+βδ+γδ)

Answer: (B)

Squaring a sum distributes across all terms and includes every cross-term twice. For four terms α, β, γ, δ this gives α^2+β^2+γ^2+δ^2 + 2(αβ+αγ+αδ+βγ+βδ+γδ). That expanded form matches the square of the sum exactly. The simplest way to express the same quantity is to keep it as the square itself, (α+β+γ+δ)^2, which is why this option is chosen. The expanded form shows all the same contributions, but the other forms miss or alter the cross terms, so they are not generally equal to the square.

Squaring a sum distributes across all terms and includes every cross-term twice. For four terms α, β, γ, δ this gives α^2+β^2+γ^2+δ^2 + 2(αβ+αγ+αδ+βγ+βδ+γδ). That expanded form matches the square of the sum exactly. The simplest way to express the same quantity is to keep it as the square itself, (α+β+γ+δ)^2, which is why this option is chosen. The expanded form shows all the same contributions, but the other forms miss or alter the cross terms, so they are not generally equal to the square.