Does anyone have a solution for the theorem in the title?

a(b - c) = ab - ac

I can come up with two separate approaches, but not one that uses only
the 6 axioms given and 4 theorems already proven.  One approach I have
uses the fact that "a x 0 = 0", and the other uses the fact that
"-(a(-c)) = ac".  The text doesn't provide a solution.

Thanks!

First prove a*0=0 as follows: a*0 = a*(0+0)=a*0 + a*0. Then subtract
a*0 from both sides to get that a*0 = 0. Secondly prove that a*(-c) =
- a*c by a*(-c) + a*c = a*(-c+c) = a*0 = 0. From this equation it
follows that a*(-c) = - a*c from the definition of - a*c. Finally use
these two facts as follows: a*(b-c) = a* (b+(-c)) = a*b + a*(-c) = a*b
+ ( - a*c ) = a*b - a*c.