Cyclic Factorisation!

How can we factorize cyclic polynomials like $(a-b)^5 + (b-c)^5 + (c-a)^5$ ?

#Algebra

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Still no comments @Calvin Lin

Toshit Jain - 4 years, 3 months ago

What have you done? What have you tried?

Calvin Lin Staff - 4 years, 3 months ago

That's what I am asking for.. If I get a basic idea about how to start then I can proceed furher! However , I have tried to expand the expressions and then factorize but it's very tedious and time consuming and provides no output ! So , I am looking for a more efficient and reliable solution... Thanks!

Toshit Jain - 4 years, 3 months ago

Precisely, see How to ask for help in solving a particular problem to understand how to phrase your questions to get a better reply.

Are you demanding the answer of the factorization?
Are you asking about the general approach?
What do you know so far? Do we have to explain how expanding algebraic terms works?
What various options would you try? Do we have to explain how "brute force" works?

If you provide more details about what you know and what you're looking for, then people can respond accordingly. Right now, it seems like "I'm lazy. Factorize this for me. I can't even be bothered to put it into Mathematica."

Try rephrasing your question with more details.

Calvin Lin Staff - 4 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$