Giải thích các bước giải:
`(a+b+c)^3-(a+b-c)^3-(b+c-a)^3-(c+a-b)^3`
Đặt `a+b-c=x;b+c-a=y;c+a-b=z`
`=>x+y+z=a+b-c+b+c-a+c+a-b=a+b+c`
`=>(a+b+c)^3-(a+b-c)^3-(b+c-a)^3-(c+a-b)^3`
`=(x+y+z)^3-x^3-y^3-z^3`
`=x^3+y^3+z^3+3xy(x+y)+3z(x+y)(x+y+z)-x^3-y^3-z^3`
`=3xy(x+y)+3z(x+y)(x+y+z)`
`=3(x+y)(xy+xz+zy+z^2)`
`=3(x+y)[x(y+z)+z(y+z)]`
`=3(x+y)(y+z)(x+z)`
`=3(a+b-c+b+c-a)(b+c-a+c+a-b)(a+b-c+c+a-b)`
`=3.2b.2c.2a`
`=24abc vdots 24`
Vậy `(a+b+c)^3-(a+b-c)^3-(b+c-a)^3-(c+a-b)^3vdots24.`