Show that the product of two transpositions can be expressed as a product of $3$-cycles Consider the symmetric group $S_n$ where $n>2.$ 
Show that the product of two transpositions $(ab),\,(cd)$ can be written as a product of $3$-cycles where $a,b,c,d$ are all distinct.
I'm not sure where a sensible place to start is so any suggestions would be appreciated.

Try $(ab)(cd) = (ab)(bc)(bc)(cd)= (abc)(bcd)$.
