a(b2 - c2) + b(c2-a2) + c(a2-b2)
=a(b2-c2) + b(a2-b2+b2-c2) + c(a2-b2)
=a(b2-c2) - b[(a2-b2)+(b2-c2)] + c(a2-b2)
=a(b2-c2) - b(a2-b2) - b(b2-c2) + c(a2-b2)
=[a(b2-c2) - b(b2-c2)] - [b(a2-b2)-c(a2-b2) ]
=(b2-c2)(a-b) - (a2-b2)(b-c)
=(a-b)(b-c)(b+c) - (a+b)(a-b)(b-c)
=(a-b)(b-c)[(b+c)-(a+b)]
=(a-b)(b-c)(c-a)