# 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>\displaystyle {xy}+{xk}+{yj}+{jk}=(x+j)(y+k)</math>. | + | The general statement of SFFT is: <math>\displaystyle {xy}+{xk}+{yj}+{jk}=(x+j)(y+k)</math>. Two special cases appear most commonly: <math>\displaystyle xy + x + y + 1 = (x+1)(y+1)</math> and <math>\displaystyle xy - x - y +1 = (x-1)(y-1)</math>. |

== Applications == | == Applications == |

## Revision as of 13:38, 23 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: . Two special cases appear most commonly: and .

## 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.