#1907 · Algebra · Polynomials

Identity with fourth powers

Prove that $4 {α^{4} + β^{4} + γ^{4} + (α + β + γ)^{4}} = (β + γ)^{4} + (γ + α)^{4} + (α + β)^{4} + 6 (β + γ)^{2} (γ + α)^{2} + 6 (γ + α)^{2} (α + β)^{2} + 6 (α + β)^{2} (β + γ)^{2}$ .

~20 minProof · checked by AIAlgebraic identitiesSymmetric functions

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Miscellaneous Examples, No. 294 (part 2)

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