化简(x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)=_______

问题描述:

化简(x-1)(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^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^8-1)(x^8+1)(x^16+1)
=(x^16-1)(x^16+1)
=x^32-1

原式=(x^2-1)(x^2+1)````(x^16+1)
=x^32-1