[tex] \sf \pink{a(b-c)+b(c-a)+c(a-b) }\\[/tex]
[tex] \sf =ab -ac +bc -ba +ca -cb\\[/tex]
[tex] \sf =ab -ac +bc -ab +ac -bc \\[/tex]
[tex] \sf = \cancel{ab} - \cancel{ac} + \cancel{bc} - \cancel{ab} + \cancel{ac} - \cancel{bc} \\[/tex]
[tex] \sf \pink{=0} [/tex]
