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

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

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

Answer: (B)

When you square a sum of three terms, cross terms appear. Expand (α + β + γ)² to get α² + β² + γ² + 2αβ + 2βγ + 2αγ. To isolate the sum of squares, move the cross terms to the other side: α² + β² + γ² = (α + β + γ)² − 2(αβ + βγ + αγ). This is exactly the expression that matches how α² + β² + γ² relates to the total sum and the pairwise products. The other forms would either still include cross terms or only restate the left-hand side without linking it to α + β + γ and the products.

When you square a sum of three terms, cross terms appear. Expand (α + β + γ)² to get α² + β² + γ² + 2αβ + 2βγ + 2αγ. To isolate the sum of squares, move the cross terms to the other side: α² + β² + γ² = (α + β + γ)² − 2(αβ + βγ + αγ). This is exactly the expression that matches how α² + β² + γ² relates to the total sum and the pairwise products. The other forms would either still include cross terms or only restate the left-hand side without linking it to α + β + γ and the products.