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1+2乘以1+2的平方乘以1+2的四次方乘以1+2的八次方怎么算?
题目详情
1+2乘以1+2的平方乘以1+2的四次方乘以1+2的八次方怎么算?
▼优质解答
答案和解析
(1+2)(1+2^2)(1+2^4)(1+2^8)
=(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
=(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
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