deriving sum of squares for roots of polynomials

[sudden ore]

How do i derive these formula

[dull flower]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations
4. Do not ping the mods, unless someone is breaking the rules.
5. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[tiny pike]

expand the right hand side and simplify

$(a+b)^3-3ab(a+b)=a^3+3a^2b+3ab^2+b^3-3a^2b-2ab^2=a^3+b^3$