Computational algebraic analysis demonstrates factorizations for the sum of three cubes using an eleven-variable master identity, highlighting new algebraic structures in cubic polynomials.
This paper presents a master polynomial identity with 11 variables (a, b, c, d, e, f, g, h, x, y, z) that decomposes the sum of three cubes into a product of three factors. In addition, a special case obtained via a dedicated substitution and parameter permutation is provided, along with several standalone sums of three cubes featuring a similar structural property. All identities have been symbolically verified using the SymPy library in Python. The python script "Verification.py" is attached to this record to allow direct independent verification of all equations.
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Komil Rasulov (2026) studied this question.
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