Factor expression A so that it looks like expression B

[sharpycasio]

Homework Statement

This question stems from this one: https://www.physicsforums.com/showthread.php?t=642712

I think I know how to solve it now. The only problem is I have to show how to factor this expression into the form WolframAlpha shows.

$-a^2 b + a b^2 + a^2 c - b^2 c - a c^2 + b c^2$ → $-(a-b)(a-c)(b-c)$

Homework Equations

The Attempt at a Solution

I did this but then I don't know how to proceed.

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

Please help. Thanks

 

[Sourabh N]

By rearranging it like so:
$−a^2b+ab^2+a^2c−b^2c−ac^2+bc^2 \rightarrow −a^2b+a^2c+ab^2−ac^2−b^2c+bc^2$

 

[sharpycasio]

You're a genius! Thank you. :)