Question

what is the equation of alpha + beta whole cube

Answer 1

We can write,
(α+β)^3 = (α+β)*(α+β)*(α+β)
              = (α+β)*(α^2+2αβ+β^2)
              = α^3+β^3+3αβ(α+β)
=>
(α+β)^3 -3αβ(α+β) = α^3+β^3
(α+β){(α+β)^2 -3αβ} = α^3+β^3
(α+β)(α^2+β^2+2αβ-3αβ) = α^3+β^3
(α+β)(α^2+β^2-αβ) = α^3+β^3
=>
α^3+β^3 = (α+β)(α^2+β^2-αβ)