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