How can I expand this term ∇∙(φuu)

[oxxiissiixxo]

How can I expand this term ∇∙(φuu) and ∇∙(T×u)

∇∙(φuu) where φ is a scalar and u is a vector

and

∇∙(T×u) where T is a second order tensor and u is a vector.

 

[oxxiissiixxo]

I found out that the solution for
∇∙(φuu) is φu∙∇u+u[∇∙(φu)]
for this the solution is just seemed like
∇∙(φuu) is φu∙∇u+u[∇∙(φu)]
∇∙(AB) is A∙∇B+B[∇∙(A)]
but I just can't fill in the step correctly in between
and
∇∙(T×u) is -u×(∇∙T)+T