If a+b+c=0 then prove that a^4+b^4+c^4=2(a^2b^2+b^2c^2+c^2a^2)
You might want to look at the patterns of "trinomial expansion" and its connection to Pascal's triangle
Here is a very neat webpage.
They expand (a+b+c)^5
You have to expand (a+b+c)^4
http://www.rowan.edu/open/depts/math/osler/Trinomial_triangle.pdf