#1904 · Algebra · Polynomials

Algebraic Identity Verification

If $A = a x - b y - cz$ , $D = b z + cy$ , $B = b y - cz - a x$ , $E = c x + a z$ , $C = cz - a x - b y$ , $F = a y + b x$ , prove that $A B C - A D^{2} - B E^{2} - C F^{2} + 2 D E F = (a^{2} + b^{2} + c^{2}) (a x + b y + cz) (x^{2} + y^{2} + z^{2})$ .

~25 minProof · checked by AIalgebraic identitiespolynomial manipulation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Miscellaneous Examples, No. 299

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