Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th
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  Let f(x)=xn+an. In order to prove that x+a is a factor of f(x) for any odd positive integer n, it is sufficient to show that f(−a)=0. f(−a)=(−a)n+an=(−1)nan+an f(−a)=(−1+1)an           [ n is odd positive integer ] f(−a)=0×an=0 Hence, x+a is a factor of xn+an, when n is an odd positive integer.
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