#1418 · Algebra · Polynomials

Sum of odd and even terms

If $A$ be the sum of the odd terms and $B$ the sum of the even terms in the expansion of $(x + a)^{n}$ , prove that $A^{2} - B^{2} = (x^{2} - a^{2})^{n}$ .

~10 minProof · checked by AIBinomial TheoremAlgebraic identities

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIII. Binomial Theorem: Positive Integral Index, Examples XIII.b, No. 8

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