Order of operations and the BODMAS are fundamental to all tenets of maths, but, in the interest of time-saving, can shortcuts be allowed, especially one when already knows the end result?
Supposed I would like to re-write the expression $a[b(c-d)]$ as $ab(c-d)$.
I could of course immediately do so i.e. $a[b(c-d)]$ = $ab(c-d)$ by multiplying $a$ in directly.
However, this might not strictly follow the BODMAS rule because I did not deal with what was in the inner brackets first. If I follow the BODMAS rule which means I must tackle what's in inner the brackets first, I would write:
$a[b(c-d)]=a(bc-bd)=abc-abd=ab(c-d)$
This however, seems unnecessarily trivial and time-wasting at college-level mathematics especially when I know what the end-result will already be.
Would like to seek advice on this - must the long way always be taken?