using binomial theorem prove that (x^n-y^n) is divisible by (x-y)

     xn = x-y+ynxn = x-y+ynxn = x-yn+C1nx-yn-1.y +C2nx-yn-2.y2 + .....+Cn-1nx-y.yn-1 +Cnn.ynxn = x-yn+C1nx-yn-1.y +C2nx-yn-2.y2 + .....+Cn-1nx-y.yn-1 +ynxn-yn = x-yn+C1nx-yn-1.y +C2nx-yn-2.y2 + .....+Cn-1nx-y.yn-1 xn-yn =x-yx-yn-1+nyx-yn-2 + ....+Cn-1nyn-1So, xn-yn is clearly divisible by x-y.

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