Đặt : x-y =a , y-z = b ===> z-x = -(a+b)
(x-y)^5+ (y-z)^5+ (z-x)^5 = a^5 + b^5 [-(a+b)]^5 = a^5 + b^5 - (a+b)^5
= a^5 + b^5 - (a^5 + 5a^4*b + 10a^3*b^2 + 10a^2*b^3 + 5a*b^4 + b^5)
= -( 5a^4*b +10a^3*b^2 + 10a^2*b^3 + 5a*b^4)
=-5ab( a^3+ 2a^2*b + 2a*b^2 + b^3)
= - 5ab[(a+b)*(a^2+b^2-ab) + 2ab*(a+ b) ]
= - 5ab*(a+ b)*(a^2+ab +b^2)
nguồn: yahooo