CM: a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2)-ab-bc-ca Thank!!

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1. `a^3+b^3+c^3-3abc`

   `⇔a^3+3a^2b+3ab^2+b^3-3a^b-3ab^2-3abc+c^3`

   `⇔(a+b)^3-3ab(a+b)+c^3-3abc`

   `⇔(a+b+c)[(a+b)^2-c(a+b)+c^2]-3ab(a+b+c)`

   `⇔(a+b+c)(a^2+b^2+c^2+2ab-ca-cb)-3ab(a+b+c)`

   `⇔(a+b+c)(a^2+b^2+c^2-ca-cb+2ab-3ab)`

   `⇔(a+b+c)(a^2+b^2+c^2-ab-bc-ca)`

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2.   a³ + b³ + c³ – 3abc

   =(a + b)(a² – ab + b²) + c³ – 3abc

   =(a + b)(a² – ab + b²) + c(a² – ab + b²) – 2abc – ca² – cb²

   =(a + b + c)(a² – ab + b²) – (abc + b²c + bc² + ac² + abc + c²a) + c³ + ac² + bc²

   =(a + b = c)(a² – ab + b²) – (a + b + c)(bc + ca) + c²(a + b + c)

   =(a + b + c)(a² + b² + c² – ab – bc – ca)

   “Chúc bạn học tốt nha!!”

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