Difference between revisions of "Sum and difference of powers"

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The '''sum and difference of cubes''' identities refer to two powerful factoring techniques that, respectively, factor a sum of cubes and a difference of cubes.
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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 Cubes==
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==Factored Forms of Sums and Differences of Powers==
* <math> a^3 + b^3 = (a+b)(a^2-ab+b^2)</math>
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*<math>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}</math>
* <math>a^3-b^3 = (a-b)(a^2+ab+b^2)</math>
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*<math>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})</math>
 
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==See Also==
==See also==
 
 
* [[Factoring]]
 
* [[Factoring]]
* [[Difference of Squares]]
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* [[Difference of squares]], an extremely common specific case of this.
 
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[[Category:Elementary algebra]]
 
[[Category:Elementary algebra]]

Revision as of 20:32, 10 March 2008

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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