`a^4(b-c) + b^4(c-a) + c^4(a-b)`
`<=> a^4(b-a + a-c) + b^4(c-a) + c^4(a-b)`
`<=> a^4(b-a) + a^4(a-c) - b^4(a-c) - c^4(b-a)`
`<=> (b-a)(a^4 - c^4) + (a-c)(a^4-b^4)`
`<=> (b-a)(a^2 - c^2)(a^2 + c^2) + (a-c)(a^2+b^2)(a^2-b^2)`
`<=> (b-a)(a-c)(a+c)(a^2+c^2) + (a-c)(a^2+b^2)(a-b)(a+b)`
`<=> (b-a)(a-c)[(a+c)(a^2+c^2) - (a+b)(a^2+b^2)]`
`<=> (b-a)(a-c)[a^3 + ac^2 + a^2c + c^3 - a^3 - ab^2 - a^2b - b^3]`
`<=> (b-a)(a-c)[c^3 - b^3 + (ac^2-ab^2) + (a^2c - a^2b)]`
`<=> (b-a)(a-c)[(c-b)(c^2+bc+b^2) + a(c^2 - b^2) + a^2(c-b)]`
`<=> (b-a)(a-c)[(c-b)(c^2 + bc + b^2) + a(c-b)(c+b) + a^2(c-b)]`
`<=> (b-a)(a-c)(c-b)(c^2 + bc + b^2 + a(c+b) + a^2)`
`<=> (b-a)(a-c)(c-b)(a^2 + b^2 + c^2 + bc + ac + ab)`