can't figure it out-
Let $F = \Bbb{F}_2 = \{0,1\}$ and Let $f(x_1, \ldots , x_m)$ be a non-constant polynomial of total degree $d$, with individual degrees smaller than 2. Prove that:
$$1/(2^d) \le Pr [ f (a_1,\ldots, a_m) = 0] \le 1 − 1/(2^d)$$
where $a_1 ,\ldots ,a_m$ are chosen uniformly from $F$
I was suggested to prove it using induction on the total degree $d$. The basis was easy (for example, one part of the inequality can be proven directly from Schwartz–Zippel lemma) but I got stuck on the inductive step.
Help will be highly appreciated