Problem #PRU-61001

Problems Algebra Polynomials Algebraic identities for polynomials Factoring polynomials

Problem

Prove the following formulae are true: $\begin{aligned} a^{n + 1} - b^{n + 1} & = (a - b) (a^{n} + a^{n - 1} b + \dots + b^{n}); \\ a^{2 n + 1} + b^{2 n + 1} & = (a + b) (a^{2 n} - a^{2 n - 1} b + a^{2 n - 2} b^{2} - \dots + b^{2 n}) . \end{aligned}$

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