Difference between revisions of "Simon's Favorite Factoring Trick"

(Simon's Favorite Factoring Trick)
(Statement of the factorization)
Line 1: Line 1:
 
=== Statement of the factorization ===
 
=== Statement of the factorization ===
 
Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization. SFFT is: <math>{xy}+{xk}+{yj}+{jk}=(x+j)(y+k)</math>.
 
Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization. SFFT is: <math>{xy}+{xk}+{yj}+{jk}=(x+j)(y+k)</math>.
 +
 +
=== Credit ===
 +
 +
This factorization was first popularized by AoPS user ComplexZeta, whose name is Simon.
  
 
=== 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>{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.

Revision as of 21:20, 17 June 2006

Statement of the factorization

Simon's Favorite Factoring Trick (abbreviated SFFT) is a special factorization. SFFT is: ${xy}+{xk}+{yj}+{jk}=(x+j)(y+k)$.

Credit

This factorization was first popularized by AoPS user ComplexZeta, whose name is Simon.

Applications

This factorization frequently shows up on contest problems, especially those heavy on algebraic manipulation. Usually ${x}$ and ${y}$ are variables and $j,k$ are known constants. Also it is typically necessary to add the ${j}{k}$ term to both sides to perform the factorization.

Invalid username
Login to AoPS