问题
解答题
先观察下面的解题过程,然后解答问题:
题目:化简(2+1)(22+1)(24+1).
(2+1)(22+1)(24+1)=(2-1)(2+1)(22+1)(24+1)=(22-1)(22+1)(24+1)=(24-1)(24+1)=28-1.
问题:化简(3+1)(32+1)(34+1)(38+1)…(364+1).
答案
原式=
(3-1)(3+1)(32+1)(34+1)(38+1)(364+1),(4分)1 2
=
(32-1)(32+1)(34+1)(38+1)(364+1),1 2
=
(34-1)(34+1)(38+1)(364+1),1 2
=
(38-1)(38+1)(364+1),1 2
=
(364-1)(364+1),(8分)1 2
=
(3128-1).(10分)1 2