I just stumbled upon a question to figure out how to simplify
J = (ab)+(ac)-(b+c)
<=> a*(b+c) -1*(b+c)
But that was not one of the solutions. One of these was, as mentioned above, (a-1)*(b+c).
As I saw this I somehow knew it is correct, calculated it and yes it is. But my math is a bit outdated and I cannot remember the law to see this. I do know it is correct, but by the love of god, I still don't know how to pull it of.