`a(b-c)^2 + b(c-a)^2 + c(a-b)^2 – a^3 –b^3 –c^3 + 4abc

Giải thích các bước giải:

`a(b-c)^2 + b(c-a)^2 + c(a-b)^2 – a^3 –b^3 –c^3 + 4abc`

`= [a(b-c)^2-a^3+4abc] + [b(c-a)^2-b^3] + [c(a-b)^2-c^3]`

`=a [(b-c)^2-a^2+4bc] + b[(c-a)^2-b^2] + c[(a-b)^2-c^2] `

` =a [b^2-2bc+c^2-a^2+4bc] + b[(c-a-b)(c-a+b)] + c[(a-b-c)(a-b+c)] `

`= a [(b+c)^2-a^2] + b[(c-a-b)(c-a+b)] + c[(a-b-c)(a-b+c)] `

`= a [(b+c-a)(b+c+a)] + b[(c-a-b)(b+c-a)] - c[(b+c-a)(a-b+c)] `

`= (b+c-a)(ab+ac+a^2+bc-ab-b^2-ac+bc-c^2) `

`=(b+c-a)[a^2-(b^2-2bc+c^2)] `

`=(b+c-a)[a^2-(b-c)^2] `

`=(b+c-a)(a-b+c)(a+b-c) `