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1. Show that x-y is a factor of x^n-y^n

Through empircal testing, i figured out the other factor must be x^(n-1) + x^(n-2)y + x^(n-3)y^2 + ... + y^(n-1), though i can't come up with a prove for it..

2. Prove that (x+a) is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5

3. prove that (x-a) is a factor of x^3 - (a+b+c)x^2 + (ab+bc+ca)x - abc

the last two i have no idea where to begin.. Can someone please help me? thanks :D