User:Lokhinwan/sandbox

$$-(a-b)(b-c)(c-a) =(b-a)(b-c)(c-a) =(b^2-bc-ba+ac)(c-a) =cb^2-bc^2-abc+ac^2-ab^2+abc+ba^2-ca^2 =ba^2-ab^2+cb^2-bc^2+ac^2-ca^2 =(ba^2-ab^2)+(cb^2-bc^2)+(ac^2-ca^2) =ab(a-b)+bc(b-c)+ca(c-a) $$