Difference between revisions of "Factoring"

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(This is not a recognized formula, please do not quote it on the USAMO or similar national proof contests)
 
(This is not a recognized formula, please do not quote it on the USAMO or similar national proof contests)
 
===Summing Series===
 
===Summing Series===
Also, it is helpful to know how to sum [[Arithmetic Series]] and [[Geometric Series]].
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Also, it is helpful to know how to sum [[arithmetic series]] and [[geometric series]].

Revision as of 13:17, 18 June 2006

Note to readers and editers: Please fix up this page by adding in material from Joe's awesome factoring page.


Why Factor

Factoring equations is an essintial part of problem solving. Applying number theory to products yields many results.

There are many ways to factor.

Difference of Squares

$a^2-b^2=(a+b)(a-b)$

Difference of Cubes

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Sum of Cubes

$a^3+b^3=(a+b)(a^2-ab+b^2)$

Simon's Trick

See Simon's Favorite Factoring Trick (This is not a recognized formula, please do not quote it on the USAMO or similar national proof contests)

Summing Series

Also, it is helpful to know how to sum arithmetic series and geometric series.

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