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(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)为什么要除

题目详情
(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)
为什么要除以(a-1)
▼优质解答
答案和解析
因为乘了一个a-1,这样就可以连续用平方差公式,所以为了保持恒等,还要除以一个a-1