I am trying to express the wedge product $$p\wedge q\wedge r$$ into a sum of tensor products, where $p$, $q$, $r$ are one forms.
I know that the wedge product $p \wedge q$ for one forms is $$p\wedge q= p\otimes q-q\otimes p.$$
Using the associative rule for wedge product, I get $$p\wedge q\wedge r=(p \wedge q) \wedge r= (p\otimes q-q\otimes p)\wedge r.$$
How can I prodceed further? What rule tells us how to combine wedge products and tensor products?
I intuitively think the next step should be
$$(p\otimes q-q\otimes p)\wedge r= (p\otimes q) \wedge r-(q \otimes p)\wedge r,$$ but I am not sure if this is a valid operation.