| 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)。 解:(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)。 |
解:原式=
(3﹣1)(3+1)(32+1)(34+1)(38+1)(364+1),
=
(32﹣1)(32+1)(34+1)(38+1)(364+1),
=
(34﹣1)(34+1)(38+1)(364+1),
=
(38﹣1)(38+1)(364+1),
=
(364﹣1)(364+1),
=
(3128﹣1)。
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