Difference between revisions of "Simon's Favorite Factoring Trick"
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== Statement of the factorization == | == Statement of the factorization == | ||
| − | The general statement of SFFT is: <math>{xy}+{xk}+{yj}+{jk}=(x+j)(y+k)</math>. More oftenly however SFFT is introduced as <math>xy + x + y + 1 = (x+1)(y+1)</math> or <math> xy - x - y +1 = (x-1)(y-1)</math>. | + | The general statement of SFFT is: <math>\displaystyle {xy}+{xk}+{yj}+{jk}=(x+j)(y+k)</math>. More oftenly however SFFT is introduced as <math>\displaystyle xy + x + y + 1 = (x+1)(y+1)</math> or <math>\displaystyle xy - x - y +1 = (x-1)(y-1)</math>. |
== Applications == | == Applications == | ||
| − | This factorization frequently shows up on contest problems, especially those heavy on algebraic manipulation. Usually <math>{x}</math> and <math>{y}</math> are variables and <math>j,k</math> are known constants. Also it is typically necessary to add the <math>{j}{k}</math> term to both sides to perform the factorization. | + | This factorization frequently shows up on contest problems, especially those heavy on algebraic manipulation. Usually <math>\displaystyle {x}</math> and <math>\displaystyle {y}</math> are variables and <math>\displaystyle j,k</math> are known constants. Also it is typically necessary to add the <math>\displaystyle {j}{k}</math> term to both sides to perform the factorization. |
== Examples == | == Examples == | ||
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=454191#p454191 AIME 1987/5] | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=454191#p454191 AIME 1987/5] | ||
Revision as of 21:18, 21 June 2006
Introduction
Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization first popularized by AoPS user Simon Rubinstein-Salzedo. This appears to be the thread where Simon's favorite factoring trick was first introduced.
Statement of the factorization
The general statement of SFFT is: 
. More oftenly however SFFT is introduced as 
or 
.
Applications
This factorization frequently shows up on contest problems, especially those heavy on algebraic manipulation. Usually 
and 
are variables and 
are known constants. Also it is typically necessary to add the 
term to both sides to perform the factorization.
