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(a+1)(a2+1)(a4+1)(a8+1)(a16+1)=?

分类: 作业答案 • 2022-04-06 14:37:29
问题描述：

(a+1)(a2+1)(a4+1)(a8+1)(a16+1)=?

答

(a+1)(a^2+1)(a^4+1)(a^8+1)(a^16+1)
=(a-1)[(a+1)(a^2+1)(a^4+1)(a^8+1)(a^16+1)]/(a-1)
=[a^2-1)(a^2+1)(a^4+1)(a^8+1)(a^16+1)]/(a-1)
=[(a^4-1)(a^4+1)(a^8+1)(a^16+1)]/(a-1)
=[(a^8-1)(a^8+1)(a^16+1)]/(a-1)
=[(a^16-1)(a^16+1)]/(a-1)
=(a^32-1)/(a-1)

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