Sum and difference of powers

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The sum and difference of powers identities refer to powerful factoring techniques that, respectively, factor a sum of cubes and a difference of certain powers.

Factored Forms of Sums and Differences of Powers

  • $a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^2+\ldots+ab^{n-2}+b^{n-1}$
  • $a^{2n+1}+b^{2n+1}=(a+b)(a^{2n}-a^{2n-1}b+a^{2n-2}b^2-\ldots-ab^{2n-1}+b^{2n})$

See Also

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