α^2 + β^2 + γ^2 + δ^2 equals which expression?

α^2 + β^2 + γ^2 + δ^2 equals which expression?

• A. (α+β+γ+δ)^2
• B. α^2+β^2+γ^2+δ^2
• C. (α+β+γ+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: (C)

When you square a sum, you get the sum of the squares plus twice the sum of all pairwise products. So for four variables, (α + β + γ + δ)² = α² + β² + γ² + δ² + 2(αβ + αγ + αδ + βγ + βδ + γδ). If you solve this for the sum of the squares, you move the cross-term part to the other side: α² + β² + γ² + δ² = (α + β + γ + δ)² − 2(αβ + αγ + αδ + βγ + βδ + γδ). This matches the expression that represents the left-hand side in terms of the square of the sum and the pairwise products. The other forms either keep the cross terms on the wrong side, or simply restate the left-hand side without rewriting it, or include the cross terms with the opposite sign, so they don’t express the sum of squares correctly in terms of the sum.

When you square a sum, you get the sum of the squares plus twice the sum of all pairwise products. So for four variables,

(α + β + γ + δ)² = α² + β² + γ² + δ² + 2(αβ + αγ + αδ + βγ + βδ + γδ).

If you solve this for the sum of the squares, you move the cross-term part to the other side:

α² + β² + γ² + δ² = (α + β + γ + δ)² − 2(αβ + αγ + αδ + βγ + βδ + γδ).

This matches the expression that represents the left-hand side in terms of the square of the sum and the pairwise products. The other forms either keep the cross terms on the wrong side, or simply restate the left-hand side without rewriting it, or include the cross terms with the opposite sign, so they don’t express the sum of squares correctly in terms of the sum.