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

问题描述:

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)