Đáp án:
`-3(a-b)(a-c)(b-c)`
Giải thích các bước giải:
`(a-b)³+(b-c)³+(c-a)³`
`=a³-3a²b+3ab²-b³+b³-3b²c+3bc²-c³+c³-3c²a+3ca²-a³`
`=(a³-a³)-3a²b+3ab²+(-b³+b³)-3b²c+3bc²+(-c³+c³)-3c²a+3ca²`
`=-3a²b+3ab²-3b²c+3bc²-3c²a+3ca²`
`=-3(a²b-ab²+b²c-bc²+c²a-ca²)`
`=-3[(a²b-ab²)+(c²a-bc²)-(ca²-b²c)]`
`=-3[ab(a-b)+c²(a-b)-c(a²-b²)]`
`=-3[ab(a-b)+c²(a-b)-c(a+b)(a-b)]`
`=-3{(a-b)[ab+c²-c(a+b)]}`
`=-3[(a-b)(ab+c²-ac-bc)]`
`=-3{(a-b)[(ab-bc)-(ac-c²)]}`
`=-3{(a-b)[b(a-c)-c(a-c)]}`
`=-3(a-b)(a-c)(b-c)`