(2+1)(22+1)(24+1)(28+1)=?不用计算器,幂的形式

2025-06-28 00:59:22
推荐回答(1个)
回答1:

用平方差
乘以1,即2-1
则原式=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
=(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