In reply to that expanding one, the actual answer to the question is also quite funny; (a+b)^n expands to:
a^n +
nab + b^n
Made me laugh more when I saw that then when I saw the picture
EDIT: Yeah, need to L2Maths better, that only works on the first expansion, not to the nth expansion. Uni has made me thick.
Total expansion is:
a^n + (n-1)ba^(n-1) + ab^(n-1) + a^(n-1)b + (n-1)ab^(n-1) + b^n
(Yay, I can still maths)