Question

simplify a(a-b)+b(b-c)+c(c-a)​

Answer 1

Given: The term a(a-b)+b(b-c)+c(c-a)​

To find: Simplify the given term.

Solution:

• Now we have given the term a(a-b)+b(b-c)+c(c-a)​

• Now multiplying inside, we get:

                 a^2 - ab + b^2 - bc + c^2 - ac

                 a^2 + b^2 + c^2 - ab - bc - ac

• Now multiplying and dividing this by 2, we get:

                 1/2 x { 2 ( a^2 + b^2 + c^2 - ab - bc - ac ) }

                 1/2 x { 2a^2 + 2b^2 + 2c^2 - 2ab - 2bc - 2ac }

                 1/2 x { (a^2 + b^2 - 2ab) + (b^2 + c^2 - 2bc) + (c^2 + a^2 - 2ac) }

                 1/2 x { (a - b)^2 + (b - c)^2 + (c - a)^2 }

Answer:

            So simplifying a(a-b)+b(b-c)+c(c-a)​, we get:

            1/2 x { (a - b)^2 + (b - c)^2 + (c - a)^2 }