The teacher has said that the hardest question is on roots and coeffients. We are allowed to bring in a sheet with anything we want on it...

I'm planning on taking in ones with the answers to some roots and coeffients, such as a^2 + b^2 + c^2 = (a + b + c)^2 -2(ab + ac + bc) (improvise those letters as alpha etc...)

If possible, I would to know these in the form similar to that above (working would be appreciated):

1) a^3 + b^3 + c^3

2) a^2 + b^2 +c^2 + d^2

3) a^3 + b^3 +c^3 + d^3

Any other common/known types would be appreciated.

Also, could some1 please list the different types of possibilites (not like above), such as where 1 root is twice the other. No need for working, just the different types youve seen...