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=

1
2
(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)

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