Question

（3+1）（3²+1）（3四次方+1）（3八次方+1）（3十六次方+1）

Answer 1

用平方差
原式=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3-1)
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/2
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)/2
=(3^8-1)(3^8+1)(3^16+1)/2
=(3^16-1)(3^16+1)/2
=(3^32-1)/2

追问

后面为什么/2？？？？？？？

追答

分子上乘以了(3-1)，所以要除以2

追问

哦哦哦

Answer 2

原式=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3-1)
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3-1)
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)/(3-1)
=(3^8-1)(3^8+1)(3^16+1)/(3-1)
=(3^16-1)(3^16+1)/2
=(3^32-1)/2