化简:(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1).

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/30 02:09:28
化简:(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1).

化简:(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1).
化简:(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1).

化简:(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1).
原式=(x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(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)

原式=[(x－1)(x＋1)(x²＋1)(x^4＋1)(x^8＋1)(x^16)＋1]/(x－1) 【连续使用平方差公式】
=[x^32－1]/(x－1)

将该式当做一个分子为原式、分母为1的分式，分子分母同乘以(x-1)可化简得答案。

（x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)
=（x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(x-1)
=(x^2-1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(x-1)
=……
=(x^32-1)/(x-1)

(x-1)/(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(x-1).
=(x^2-1)(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-81)(x^8+1)(x^16+1)
=(x^16-1)(x^16+1)
=(x^32+1)

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