Toán em hãy xây dưng HĐT: (a+b+c)^3 = ??? => a^3 + b^3 + c^3 = ??? 30/06/2021 By Madelyn em hãy xây dưng HĐT: (a+b+c)^3 = ??? => a^3 + b^3 + c^3 = ???
`(a+b+c)^3` `=[(a+b)+c]^3` `=(a+b)^3+3(a+b)^2c+3(a+b)c^2+c^3` `=a^3+3a^2b+3ab^2+b^3+3c(a^2+2ab+b^2)+3ac^2+3bc^2+c^3` `=a^3+b^3+c^3+3a^2b+3ab^2+3b^2c+3bc^2+3c^2a+3ca^2+6abc` ——————————————————————— `=> a^3+b^3+c^3=(a+b+c)^3-3(a+b)^2c-3(a+b)c^2-3ab(a+b)` `=(a+b+c)^3-3c(a+b)(a+b+c)-3ab(a+b)` `=(a+b+c)^3-3(a+b)(ac+bc+c^2+ab)` `=(a+b+c)^3-3(a+b)[a(b+c)+c(b+c)]` `=(a+b+c)^3-3(a+b)(b+c)(c+a)` Trả lời
`(a+b+c)^3`
`=[(a+b)+c]^3`
`=(a+b)^3+3(a+b)^2c+3(a+b)c^2+c^3`
`=a^3+3a^2b+3ab^2+b^3+3c(a^2+2ab+b^2)+3ac^2+3bc^2+c^3`
`=a^3+b^3+c^3+3a^2b+3ab^2+3b^2c+3bc^2+3c^2a+3ca^2+6abc`
———————————————————————
`=> a^3+b^3+c^3=(a+b+c)^3-3(a+b)^2c-3(a+b)c^2-3ab(a+b)`
`=(a+b+c)^3-3c(a+b)(a+b+c)-3ab(a+b)`
`=(a+b+c)^3-3(a+b)(ac+bc+c^2+ab)`
`=(a+b+c)^3-3(a+b)[a(b+c)+c(b+c)]`
`=(a+b+c)^3-3(a+b)(b+c)(c+a)`