化简(x-1)(x+1)(x^2+1)(x^4+1)…(x^64+1)
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![化简(x-1)(x+1)(x^2+1)(x^4+1)…(x^64+1)](/uploads/image/z/7801799-23-9.jpg?t=%E5%8C%96%E7%AE%80%28x-1%29%28x%2B1%29%28x%5E2%2B1%29%28x%5E4%2B1%29%E2%80%A6%EF%BC%88x%5E64%2B1%29)
化简(x-1)(x+1)(x^2+1)(x^4+1)…(x^64+1)
化简(x-1)(x+1)(x^2+1)(x^4+1)…(x^64+1)
化简(x-1)(x+1)(x^2+1)(x^4+1)…(x^64+1)
(x-1)(x+1)(x^2+1)(x^4+1)…(x^64+1)
=(x^2-1)(x^2+1)(x^4+1)…(x^64+1)
=(x^4-1)(x^4+1)…(x^64+1)
=(x^8-1)……(x^64+1)
=……
=x^128-1
应用平方差公式:(x-1)(x+1) = x^2-1
(x-1)(x+1)(x^2+1)=x^4-1
(x-1)(x+1)(x^2+1)(x^4+1)=x^8-1....
最后可得(x^64-1)(x^64+1)=x^128-1
(x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)……(x^32+1)(x^64-1)
=(x^2-1)(x^2+1)(x^4+1)(x^8+1)……(x^32+1)(x^64-1)
=(x^64-1)^2
(a-1)(a+1)=a^2-1这个公式
一次类推。。最终答案应该是:x^128-1