Question

化简:(x+1)(x^2+1)(x^4+1)…(x^2009+1)(x-1)

^指乘方

Answer 1

化禅备简:(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)...…(x^1024+1)(x^2009+1)(x-1)
解：贺闹毁原式=(x-1)(x+1)(x²+1)(x⁴弯团+1).......(x^1024+1)(x^2009+1)
=(x²-1)(x²+1)(x⁴+1)........(x^1024+1)(x^2009+1)
=(x⁴-1)(x⁴+1)........(x^1024+1)(x^2009+1)
=(x^2048-1)(x^2009+1)

Answer 2

(x+1)(x^2+1)(x^4+1)…孝州闹(x^2009+1)(x-1)
=(x+1)(x-1)(x^2+1)(x^4+1)…(x^2009+1)
=(x^2-1)(x^2+1)(x^4+1)…迹顷(x^2009+1)
=……巧罩
=x^4018-1

Answer 3

:(x+1)(x^2+1)(x^4+1)…(x^2009+1)(x-1)
=﹙x－1﹚(x+1)(x^2+1)(x^4+1)…(x^2009+1)
=﹙x²－1﹚(x^2+1)(x^4+1)…(x^2009+1)
=﹙x^4－1﹚纯销﹙x^4＋1﹚宏老·····﹙x^2009＋1﹚
=﹙x^8－1﹚···﹙x^2009＋1﹚
题目再看看，有蔽裤升问题

Answer 4

（汪含游x-1)（x+1)(x^2+1)(x^4+1)…(x^2009+1)
=（老做x^2-1)(x^2+1）困销(x^4+1)…(x^2009+1)
=x^4018-1