Question

add the product:a(a-b) ,b(b-c), c(c-a)

Answer 1

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

Step-by-step explanation:

a(a-b) = a^2 - ab

b(b-c) = b^2 - bc

c(c-a) = c^2 - ac

their sum = a^2+b^2+c^2 - ab - bc - ac

Answer 2

Concept

Subtraction, multiplication, and division are the other three basic operations of arithmetic. The total amount or sum of two whole numbers is obtained by adding their values.

Given

$a(a-b) ,b(b-c), c(c-a)$

Find

We are asked to add the product

Solution

Expand each product

$a(a-b)=a^{2}-ab\\ b(b-c)=b^{2}-bc\\ c(c-a)=c^{2}-ac$

Now we will add each product

$a^{2}-ab+b^{2}-bc+c^{2}-ac$

Hence the sum is

$a^{2}-ab+b^{2}-bc+c^{2}-ac$