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Indeed, you can check that $f$ and $g$ take the same values in \emph{all}  vectors of $(\Fb)^3$, so  that  $$f (x, y, z) (\overline{x}, \overline{y}, \overline{z})  = g(x, y, z), g(\overline{x}, \overline{y}, \overline{z}),  \; \forall (x, y, z) (\overline{x}, \overline{y}, \overline{z})  \in (\Fb)^3.$$ Hence, $f$ and $g$ are \textbf{distinct} as polynomials, polynomials in $\Fb[x,y,z]$,  but they are \textbf{equal} as boolean  functions, since given an input, they return the same output! \\  \smallskip    The unexpected behaviour of the above functions $f$ and $g$ comes from the fact that   $u^2 = u$ for any $u \in \Fb $.   More generally, Therefore,  every polynomial function from $(\Fb)^3$ to $\Fb$ can be written as a polynomial $h \in \Fb[x,y,z]$  where the degree of   every variable is at most one, $0 \leq \deg_x(h),\deg_y(h),\deg_z(h) \leq 1$,  for example, $x^3 y^2 + z^{10} xy^2 = xy + zxy$, when evaluated at $3$-tuples of bits.  \begin{Definition}\label{ANF}  A \emph{squarefree} monomial is a monomial where each variable appears with exponent at most one.