$\begin{array}{l}\text { 1・147 Simplify } \\ \quad(2+1)\left(2^{2}+1\right)\left(2^{4}+1\right)\left(2^{8}+1\right) \cdots \cdots\left(2^{256}+1\right) .\end{array}$
[Solution] $\begin{aligned} \text { Original expression } & =(2-1)(2+1)\left(2^{2}+1\right)\left(2^{4}+1\right) \cdots\left(2^{256}+1\right) \\ & =2^{512}-1 .\end{aligned}$