Add the product: a(a−b), b(b−c), c(c−a)

Here we have the expressions a(a-b),b(b-c) and c(c-a)

Using the distributive law a(a-b) = a²-ab,b(b-c) = b²-bc and c(c-a) = c²-ca

Now we add the terms (a²-ab) + (b²-bc) + (c²-ca)

= a² + b² + c²-ab-bc-ca

Hence addition of the product of the above expressions is a² + b² + c²-ab-bc-ca.