  A degree-$d$ polynomial $p$ in $n$ variables over a field $\F$ is {\em
equidistributed} if it takes on each of its $|\F|$ values close to equally
often, and {\em biased} otherwise. We say that $p$ has a {\em low rank} if it
can be expressed as a bounded combination of polynomials of lower degree. Green
and Tao [gt07] have shown that bias imply low rank over large fields (i.e. for
the case $d < |\F|$). They have also conjectured that bias imply low rank over
general fields. In this work we affirmatively answer their conjecture. Using
this result we obtain a general worst case to average case reductions for
polynomials. That is, we show that a polynomial that can be {\em approximated}
by few polynomials of bounded degree, can be {\em computed} by few polynomials
of bounded degree. We derive some relations between our results to the
construction of pseudorandom generators, and to the question of testing concise
representations.
