Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "Factoring"
m (removed capitalization of internally linked terms at end.)
Line 17: Line 17:
 
(This is not a recognized formula, please do not quote it on the USAMO or similar national proof contests)
 
(This is not a recognized formula, please do not quote it on the USAMO or similar national proof contests)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]].
+
Also, it is helpful to know how to sum [[arithmetic series]] and [[geometric series]].

Revision as of 12:17, 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See Simon's Favorite Factoring Trick (This is not a recognized formula, please do not quote it on the USAMO or similar national proof contests)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.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Factoring&oldid=2634"