Câu 11:
`(a+b+c)^3=[(a+b)+c]^3`
`=(a+b)^3+3c(a+b)^2+3c^2(a+b)+c^3`
`=(a+b)^3+3c(a+b)(a+b+c)+c^3`
`=a^3+3a^2b+3ab^2+b^3+3c(a+b)(a+b+c)+c^3`
`=a^3+b^3+c^3+3ab(a+b)+3c(a+b)(a+b+c)`
`=a^3+b^3+c^3+3(a+b)(ab+ac+bc+c^2)`
`=a^3+b^3+c^3+3(a+b)[a(b+c)+c(b+c)]`
`=a^3+b^3+c^3+3(a+b)(b+c)(c+a)`
Câu 12:
`a+b+c=0`
`<=>a+b=-c`
`<=>(a+b)^3=(-c)^3`
`<=>a^3+3a^2b+3ab^2+b^3=-c^3`
`<=>a^3+b^3+c^3=-3a^2b-3ab^2`
`<=>a^3+b^3+c^3=-3ab(a+b)`
`<=>a^3+b^3+c^3=-3ab.(-c)` (do `a+b+c=0`)
`<=>a^3+b^3+c^3=3abc`
