If a+b+c = 0 show that (2a-b)^3 + (2b-c)^3 + (2c-a)^3 = 3 (2a-b)(2b-c)(2c-a)

Please help.

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- Oct 1st 2013, 07:13 PMmagakrivChallenging factorization question?
If a+b+c = 0 show that (2a-b)^3 + (2b-c)^3 + (2c-a)^3 = 3 (2a-b)(2b-c)(2c-a)

Please help. - Oct 1st 2013, 08:06 PMPlatoRe: Challenging factorization question?
Use this webpage to help do the algebra.

- Oct 1st 2013, 10:39 PMSorobanRe: Challenging factorization question?
Hello, magakriv!

Quote:

. .

Note that: /

We have: .

Cube both sides: .

. .

Since , we have:

. .

. . . . . .

. . . . . .

Back-substitute: .

- Oct 1st 2013, 10:42 PMthevinhRe: Challenging factorization question?
- Oct 1st 2013, 11:37 PMibduttRe: Challenging factorization question?