Simon's Favorite Factoring Trick

Revision as of 21:20, 17 June 2006 by Chess64 (talk | contribs) (Statement of the factorization)

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.

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