`2(a-b)(c-b)+2(b-a)(c-a)+2(b-c)(a-c)`
`=(2a-2b)(c-b)+(2b-2a)(c-a)+(2b-2c)(a-c)`
`=2ac-2ab-2bc+2b²+2bc-2ab-2ac+2a²+2ab-2bc-2ac+2c²`
`=2a²+2b²+2c²+(-2ab-2ab+2ab)+(-2bc+2bc-2bc)+(2ac-2ac-2ac)`
`=2a²+2b²+2c²-2ab-2bc-2ac`
`=a²+a²+b²+b²+c²+c²-2ab-2bc-2ac`
`=(a²-2ab+b²)+(b²-2bc+c²)+(a²-2ac+c²)`
`=(a-b)²+(b-c)²+(a-c)²`