Question

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

^指乘方

Answer 1

化简:(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)...…(x^1024+1)(x^2009+1)(x-1)
解：原式=(x-1)(x+1)(x²+1)(x⁴+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)…(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)…(x^2009+1)
=……
=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﹚﹙x^4＋1﹚·····﹙x^2009＋1﹚
=﹙x^8－1﹚···﹙x^2009＋1﹚
题目再看看，有问题

Answer 4

（x-1)（x+1)(x^2+1)(x^4+1)…(x^2009+1)
=（x^2-1)(x^2+1）(x^4+1)…(x^2009+1)
=x^4018-1