计算:(x+1)(x-1)(x2-x+1)(x2+x+1)

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计算:(x+1)(x-1)(x2-x+1)(x2+x+1)
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计算:(x+1)(x-1)(x2-x+1)(x2+x+1)
计算:(x+1)(x-1)(x2-x+1)(x2+x+1)

计算:(x+1)(x-1)(x2-x+1)(x2+x+1)
原式=(x^2-1)[(x^2+1)^2-x^2]
=(x^2-1)(x^4+x^2+1)
=x^6-1

根据乘法交换律:原式=(x+1)(x2-x+1)(x-1)(x2+x+1)
根据立方和差公式: =(x3+1)(x3-1)
根据平方差公式: =x6-1

(X+1)(x-1)(X2-x+1)(x2+x+1)
=(x2-1)((x2+1)2-x2)-x2)
=x6-1