Keep it simple, in your car when you switch on air conditioning , it increases fuel consumption. For the same speed lets say 50km/h , you will have a higher RPM than without AIr Conditioning.
If conditions permit, depending on the runway length, A packs off take off will generally increase the flex by 1 or 2 degrees , which means a lower thrust and N1 for take off , therefore a lower EGT consequently saving engine life.