Question

（2+1）（22+1）（24+1）（28+1）=?不用计算器,幂的形式

Answer 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