How to factorize a polynomial involving cyclic and homogeneous terms?

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To factorize the expression (a-b)^3 + (a+b)^3, one can expand both cubes and simplify the result. The correct factorization yields 2a(a^2 + 3b^2). The discussion emphasizes understanding the process of expansion and simplification, particularly in relation to cyclic and homogeneous polynomials. Clarification was sought on the steps involved in reaching the final factorized form. The conversation concludes with an acknowledgment of the provided solution.
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1. Factorize (a-b)^3 + (a+b)^3

2. Attempt of solution are involving cyclic or/and homogeneous polynomials

I want to understand this clearly, can anyone explain this? The answer is 2a(a^2+3b^2)
 
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takercena said:
1. Factorize (a-b)^3 + (a+b)^3

[I want to understand this clearly, can anyone explain this? The answer is 2a(a^2+3b^2)

Try expanding (a+b)^3 and (a-b)^3 and the simplifying, then factorizing.
 
What kind of explanation are you asking for?
 
Defennder said:
What kind of explanation are you asking for?
Oh, nevermind, and thanks
 

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