Question

разложить на множители (x-y)^3+(y-z)^3+(z-x)^3

Answer 1

(х-у)^3 +(y-z)^3 = (x-y + y-z)((x-y)^2 - (x-y)(y-z) + (y-z)^2)
(x-y)^3 + (y-z)^3 + (z-x)^3 = (x-z)((x-y)^2 - (x-y)(y-z) + (y-z)^2) - (x-z)^3 = 
(x-z)((x-y)^2 - (x-y)(y-z) + (y-z)^2 - (x-z)^2) = 
(x-z)((x-y)^2 - (x-y)(y-z) + (y-z)^2 - (x-z)^2) = ... = 3(x-z)(y-z)(y-x)
формулы: сумма кубов и квадрат разности