x^2+1)(x^4+1)(x^8+1)(x^16+1).将（x-1)/(x-1)乘这个整式．用平方差公式解 ,(x^2+1)(x^4+1)(x^8+1)(x^16+1).将（x-1)/(x-1)乘这个整式．用平方差公式解

把（x^2+1)(x^4+1)(x^8+1)(x^16+1)先乘（x²-1）得
（x²-1）（x^2+1)(x^4+1)(x^8+1)(x^16+1)
=(x^4-1)(x^4+1)(x^8+1)(x^16+1)
=(x^8-1)(x^8+1)(x^16+1)
=(x^16-1)(x^16+1)
=x^32-1
∴（x^2+1)(x^4+1)(x^8+1)(x^16+1)=（x^32-1）/（x²-1）
再乘（x-1)/(x-1)得
（x^32-1）/（x²-1）×（x-1)/(x-1)=

乘的确定是(x-1)/(x-1)?
我觉得应该有一个是x+1..
比如乘(x+1)/(x-1)的话,
上下再同乘(x-1)
得到(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x+1)(x-1)/(x-1)^2
=(x^2-1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(x-1)^2
=(x^4-1)(x^4+1)(x^8+1)(x^16+1)/(x-1)^2
=(x^8-1)(x^8+1)(x^16+1)/(x-1)^2
=(x^16-1)(x^16+1)/(x-1)^2
=(x^32-1)/(x-1)^2

（x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1) (分子乘以（x-1)分母除以（x-1)
=(x^2-1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(x-1)
=(x^4-1)(x^4+1)(x^8+1)(x^16+1)/(x-1)
=(x^8-1)(x^8+1)(x^16+1)/(x-1)
=(x^16-1)(x^16+1)/(x-1)
=(x^32-1)/(x-1)