Using the principle of mathematical induction. Prove that `(x^(n)-y^(n))` is divisible by (x+y) for all ` n in N`.

Explanation

P(n):`x^n−y^n` is divisble by x+y where n is even.


when n=2

`P(2):x^2−y^2` is divisible by x+y

`P(2):(x+y)(x−y)` is divisible by x+y, which is true.

Therefore P(2) is true.

when n=k+2

`x^(k+2)−y^(k+2)=x^(k+2)−x^2y^k+x^2y^k−y^(k+2)`

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