You took out only a numerical factor , when you
should have factored out an  as well.  That is,
you should have factored out , not just  

The complete factorization is:



What you did was not mathematically incorrect, it just was not
complete because the expression inside the parentheses, in
red below, can also be factored:



You can factor out an  from inside the parentheses,
like this:



and then take away the black parentheses:



and so you end up with the right answer. But it's better 
to take out  to begin with.  Then it's only
one step.

Edwin