a³+b³+c³-3abc =(a³+3a²b+3ab²+b³+c³)-(3abc+3a²b+3ab²) =[(a+b)³+c³]-3ab(a+b+c) =(a+b+c)(a²+b²+2ab-ac-bc+c²)-3ab(a+b+c) =(a+b+c)(a²+b²+c²+2ab-3ab-ac-bc) =(a+b+c)(a²+b²+c²-ab-bc-ac)
