Shannon's expansion

Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: ${\displaystyle F=x\cdot F_{x}+x'\cdot F_{x}'}$, where ${\displaystyle F}$ is any Boolean function, ${\displaystyle x}$ is a variable, ${\displaystyle x'}$ is the complement of ${\displaystyle x}$, and ${\displaystyle F_{x}}$and ${\displaystyle F_{x}'}$ are ${\displaystyle F}$ with the argument ${\displaystyle x}$ equal to ${\displaystyle 1}$ and to ${\displaystyle 0}$ respectively.

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