αβ(α+β)+βγ(β+γ)+γα(γ+α)−6αβγ=(α+β+γ)(αβ+βγ+γα)−9αβγ
You asked:
Investigate the equation: \(α \cdot β\left( α + β \right) + β \cdot γ\left( β + γ \right) + γ \cdot α\left( γ + α \right) - 6 α β γ = \left(α + β + γ\right) \cdot \left(α β + β γ + γ α\right) - 9 α β γ\).