(a + b + c).(a + b + c) - 2(a.b + b.c + c.a)
= a(a + b + c) + b(a + b + c) + c(a + b + c) - 2ab - 2bc - 2ca
= aa + ab + ca + ab + bb + bc - 2ab - 2bc - 2ca
= (2ab - ab - ab) - (2bc - bc) - (2ca - ca) + aa + bb
= 0 - bc - ca + aa + bb
= a(a - c) + b(b - c)