Question

（2+1)(2的平方+1)(2的四次方+1)(2的八次方+1)+1 等于多少

要速度，准确

Answer 1

（2+1)(2的平方+1)(2的四次方+1)(2的八次方+1)+1
=（2-1）（2+1)(2的平方+1)(2的四次方+1)(2的八次方+1)+1
=（2的平方-1)(2的平方+1)(2的四次方+1)(2的八次方+1)+1
=(2的4次方-1)(2的四次方+1)(2的八次方+1)+1
=(2的8次方-1)(2的八次方+1)+1
=2的16次方-1+1
=2的16次方

追问

=（2-1）（2+1)(2的平方+1)(2的四次方+1)(2的八次方+1)+1 这里刚开始为什么要（2-1）（2+1)

追答

凑成平方差公式

Answer 2

(2+1)(2的平方+1)(2的四次方+1)(2的八次方+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)
=(2^4-1)(2^4+1)(2^8+1)
=(2^8-1)(2^8+1)
=2^16-1

Answer 3

(2+1)(2²+1)(2⁴+1)(2^8+1)+1
=(2-1)(2+1)(2²+1)(2⁴+1)(2^8+1)+1
=(2²-1)(2²+1)(2⁴+1)(2^8+1)+1
=(2⁴-1)(2⁴+1)(2^8+1)+1
=(2^8-1)(2^8+1)+1
=(2^16-1)+1
=2^16
=65536

Answer 4

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

Answer 5

在前面添加一项2-1
原式=（2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)
=(2^4-1)(2^4+1)(2^8+1)
=(2^8-1)(2^8+1）
=2^16-1
望采纳

Answer 6

（2+1)(2的平方+1)(2的四次方+1)(2的八次方+1)+1=66536