If b is between a and c then ab+bc=ac

That's false. Take the numbers 1, 3, and 5.
Let a = 1, b = 3, and c = 5.
ab + bc = ac
3 + 15 = 5
18 ≠ 5
Since 18 does not equal 5, this is false. If you were to use the distributive property on ab + bc = ac, you would get
b(a+c) = ac, which doesn't even make sense.
Have a nice day! :)