Another option other than what Mush posted would be to take (a-1)(a-1)(a-1)(a-1)
=(a^2 - 2a +1)(a-1)(a-1)
=(a^3 -2a^2+a-a^2+2a-1)(a-1)
=(a^3-3a^2+3a-1)(a-1)
=a^4-4a^3+6a^2-4a+1
Hopefully this will help you out a little bit. Basically what you are looking to do is use the distributive property and "FOIL" the (a-1)'s out on each other.