An expansion of formula

  (a₁ + b₁)(a₂ + b₂)(a₃ + b₃)
= (a₁ + b₁){(a₂ + b₂)(a₃ + b₃)}
= (a₁ + b₁){X₁}
= a₁{X₁} + b₁{X₁}
= a₁{(a₂ + b₂)(a₃ + b₃)} + b₁{(a₂ + b₂)(a₃ + b₃)}
= a₁{(a₂ + b₂)(a₃ + b₃)}
+ b₁{(a₂ + b₂)(a₃ + b₃)}
= a₁{(a₂ + b₂)(X₂)}
+ b₁{(a₂ + b₂)(X₂)}
= a₁{a₂(X₂) + b₂(X₂)}
+ b₁{a₂(X₂) + b₂(X₂)}
= a₁{a₂(a₃ + b₃) + b₂(a₃ + b₃)}
+ b₁{a₂(a₃ + b₃) + b₂(a₃ + b₃)}
= a₁{(a₂⋅a₃ + a₂⋅b₃) + (b₂⋅a₃ + b₂⋅b₃)}
+ b₁{(a₂⋅a₃ + a₂⋅b₃) + (b₂⋅a₃ + b₂⋅b₃)}
= a₁⋅a₂⋅a₃ + a₁⋅a₂⋅b₃ + a₁⋅b₂⋅a₃ + a₁⋅b₂⋅b₃
+ b₁⋅a₂⋅a₃ + b₁⋅a₂⋅b₃ + b₁⋅b₂⋅a₃ + b₁⋅b₂⋅b₃