Đáp án:
`a(b^2 + c^2) + b(c^2 + a^2) + c(a^2 + b^2) - 2abc - a^3 - b^3 - c^3`
`= [a(b^2 + c^2) - 2abc - a^3] + bc^2 + a^2 b + a^2 c + b^2 c - b^3 - c^3`
`= a(b^2 + c^2 - 2bc - a^2) + (bc^2 - b^3) + (a^2 b + a^2 c) + (b^2 c - c^3)`
`= a[(b - c)^2 - a^2] + b(c^2 - b^2) + a^2 (b +c) + c(b^2 - c^2)`
`= a[(b - c)^2 - a^2] + b(c - b)(c +b) + a^2 (b + c) + c(b - c)(b + c)`
`= a[(b - c)^2 - a^2] + (b + c)[b(c - b) + a^2 + c(b - c)]`
`= a[(b - c)^2 - a^2] + (b + c)(bc - b^2 + a^2 + bc - c^2)`
`= - a[a^2 - (b - c)^2] + (b + c)[a^2 - (b^2 - 2bc + c^2)]`
`= - a[a^2 - (b - c)^2] + (b + c)[a^2 - (b - c)^2]`
`= - a(a - b + c)(a + b - c) + (b + c)((a - b + c)(a + b - c)`
`= (a - b + c)(a + b - c)(b + c - a)`
