Factorization of a symmetric product

Resolve into factors $(a + b + c) (b + c - a) (c + a - b) (a + b - c) (a^{2} + b^{2} + c^{2}) - 8 a^{2} b^{2} c^{2}$ .

~15 minAnswer checked instantlyFactorisationSymmetric polynomials

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Miscellaneous Examples, No. 294 (part 1)

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).