Differentisl geometry internal contraction

[pleasehelpmeno]

Hi
I am struggling to see how the relation:
(df:U)(dh:V)-(dh:V)(df:V) (1)
can be rewritten as:
U(fdh:v)-V(fdh:U)-fdh:[U,V] (2)

I have tried expanding (1) out by making a scalar vector product of Udh:V but i don't think that is right and i am just not sure how best to proceed. It was annoyingly skipped over in class today, any help or suggestions would be appreciated.

 

[Kreizhn]

I am very unclear as to what you are asking. Perhaps you could clarify? What is f,h,U,V? What does your : mean? Typically, I have seen contraction denoted by \iota or \lrcorner, so I do not know how to read this.