中學數學一問,高手請入,急.............

i.e. Identity: (x+y)(x-y) = x^2-y^2

(a-b)(a+b)(a^2+b^2)(a^4+b^4)(a^8+b^8)(a^16+b^16)..............(a^1024+b^1024)
= (a^2-b^2)(a^2+b^2)(a^4+b^4) ........... (a^1024+b^1024)
= (a^4-b^4)(a^4+b^4)........(a^1024+b^1024)
...........
...........
= (a^1024-b^1024)(a^1024+b^1024)
= a^2048-b^2048

Pan Lloyds Mathematics Companion Summer Revision S.2-S.3
Unit 5 Identities
Q.22

2010-07-17 17:52:12 補充：
I mean this exercise also contains this question.

a^2048-b^2048
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(a-b)(a+b)
=(a^2-b^2)(a^2+b^2)
=(a^4-b^4)
如止類推甘THINK:
最後應該計到...........
(a^1024-b^1024)(a^1024+b^1024)
=a^2048-b^2048
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要將個次數x2............