2+1)(2乘2+1)(4个2相乘+1)(8个2相乘+1)怎么样算简便
问题描述：
2+1)(2乘2+1)(4个2相乘+1)(8个2相乘+1)怎么样算简便
答
(2+1)(2乘2+1)(4个2相乘+1)(8个2相乘+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)
=(2^4-1)(2^4+1)(2^8+1)
=(2^8-1)(2^8+1)
=2^16-1
=65536-1
=65535