#1556 · Algebra · Polynomials

Thirds of Trinomial Expansion Coefficients

If the expansion of $(1 + x + x^{2})^{n}$ be $a_0 + a_1x + a_2x^2 +
otes + a_rx^r +
otes + a_{2n}x^{2n} $, s h e w t ha t$ a_0 + a_3 + a_6 +
otes = a_1 + a_4 + a_7 +
otes = a_2 + a_5 + a_8 +
otes = 3^{n-1}$.

~20 minProof · checked by AIcube roots of unitypolynomial expansionidentities

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XV. Multinomial Theorem, Examples XV, No. 21

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