Show that
$$(a \times b) \times (c \times d)= [a,b,d]c - [a,b,c]d.$$
I understand $[a,b,d] = a \cdot (b \times d)$ and $[a,b,c] = a \cdot (b \times c)$ but not really sure where else to go with this.
Show that
$$(a \times b) \times (c \times d)= [a,b,d]c - [a,b,c]d.$$
I understand $[a,b,d] = a \cdot (b \times d)$ and $[a,b,c] = a \cdot (b \times c)$ but not really sure where else to go with this.