Question

在学习了分式的乘除法之后,老师出了这样一道计算题:

化简:(x+1)(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

Answer 1

连续使用平方差公式：
(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^4-4)(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)(X16+1)/(X-1)
=(X^32-1)/(X-1)。

追问

正确率是百分之多少

追答

=(X^4-4)(X^4+1)(X^8+1)(X^16+1)/(X-1)
这一步写错一个数据：
=(X^4-1)(X^4+1)(X^8+1)(X^16+1)/(X-1)

追问

你还没回答我呢

追答

现在保证没问题。
(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^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)(X16+1)/(X-1)
=(X^32-1)/(X-1)。

Answer 2

X^32-1/x-1

追问

我要过程