Ok so if I have (a_x + a_y + a_z)^2 I get a_x^2 + a_y^2 + a_z^2 as the answer because the cross terms go to zero. For example a_x . a_y = 0 etc... What if I have (a_x + a_y + a_z)^3 ? Will the answer be a_x^3 + a_y^3 + a_z^3 , or will it be a_x^3 + a_y^3 + a_z^3 + a_x^2 a_y + a_x^2 a_z + a_y^2 a_x + a_y^2 a_z + a_z^2 a_x + a_z^2 a_y ? My motivation for thinking it might be the first one is that a term like a_x^2 a_y could be expanded into one like a_x . a_x . a_y and then would go to zero if we take the dot product a_x a_y . On the other hand the factor a_x . a_x is a scalar and a scalar a_x^2 times a vector a_y will remain as a_x^2 a_y . On the.. third.. hand if we take the supposed commutative properties of a dot product then (a_x . a_x) . a_z should be the same as a_x . (a_x . a_z) which I seem to argue is not the case. We cannot argue that a_x . (a_x . a_z) != 0 but we can argue that (a_x . a_x) . a_z = a_x . (a_x . a_z) = 0 ... So I guess the first anwer is the right one. Confirmation or help in the right direction would be much appreciated. Thanks.