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x^6-(x^5)y+(X^4)(y^2)-(X^3)(y^3)+(X^2)(y^4)-x(y^5)+y^6=(x+y)^6-7xy(x+y)^4 +14((xy)^2)(x+y)^2 - 7(xy)^3

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If n is an odd prime then prove,

x^n-1 - X^(n-2).y+..........-x.y^(n-2)+y^(n-1) = (x+y)^n-1 - nxy(x+y)^(n-3) +..........(-1)^((n-1)/2) . n .(xy) ^ ((n-1)/2)

Thank you very much in advance for your assistance.