How can I simplify this expression using factoring?

[jesuslovesu]

Homework Statement

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2a^2*b^2*c^2 + (a+c)^2*(a+b)^2*(b+c)^2 - a^2*c^2(a+c)^2 - (a+b)^2 * a^2 * b^2 - (b+c)^2*b^2*c^2 = 2abc(a+b+c)^3

Homework Equations

The Attempt at a Solution

Well I actually tried to expand all of the exponential terms but that ended up being a total mess and wasn't even remotely obvious... My professor said using something like (a-b)^2 = (a+b)(a-b) would help, but I don't quite see how that would help.. can anyone give me a hint?

 

[Integral]

ya only tried once? I find that I need to work through complicated expressions multiple times. Don't give up keep after it. You may want to show us some of your work. If you do pleas go to the tutorials forum and read the latex thread.

 

[Xorlev]

Try it in parts. When I solve problems that look like a mess I'll draw lines down a paper and group it by addition/subtractions. That way you're just dealing with each part individually.

$\underbrace{2a^2*b^2*c^2}_{First} + \underbrace{(a+c)^2*(a+b)^2*(b+c)^2}_{Second} - \underbrace{a^2*c^2(a+c)^2}_{Third} - \underbrace{(a+b)^2 * a^2 * b^2}_{Fourth} - \underbrace{(b+c)^2*b^2*c^2}_{Fifth} &=& \underbrace{2abc(a+b+c)^3}_{Sixth}$

Now that you've grouped off your terms. Expand these out, simplify. The solution may become obvious (or at least easier) to find. When you're done, you may be left with something as simple as a quadratic, but don't quote me on that. I've not done the problem myself.