ILL 1986 Problem 34

For each non-negative integer $n$ , $F_n(x)$ is a polynomial in $x$ of degree $n$ . Prove that if the identity $$F_n(2x)=\sum_{r=0}^{n} (-1)^{n-r} \binom nr 2^r F_r(x)$$ holds for each n, then $$F_n(tx)=\sum_{r=0}^{n} \binom nr t^r (1-t)^{n-r} F_r(x)$$