The problem asks us to simplify the expression $a(b-c) + b(c-a)$.

1. Problem Description

The problem asks us to simplify the expression $a(b-c) + b(c-a)$.

2. Solution Steps

First, we distribute $a$ in the first term and $b$ in the second term:

$a(b-c) + b(c-a) = ab - ac + bc - ba$

Since $ab$ and $ba$ are the same, we can rewrite the expression as:

$ab - ac + bc - ab$

Now we can combine like terms:

$ab - ab - ac + bc = 0 - ac + bc = bc - ac$

We can factor out a common factor of $c$ to get:

$c(b-a)$

3. Final Answer

$c(b-a)$