计算:(x+1)(x-1)(x2-x+1)(x2+x+1)
问题中的2是平方
(x+1)(x-1)(x^2-x+1)(x^2+x+1)
=(x+1)(x-1)[(x^2+1)-x][(x^2+1)+x]
=(x^2-1)[(x^2+1)^2-x^2]
=(x^2-1)(x^4+x^2+1)
=x^4(x^2-1)+(x^2-1)(x^2+1)
=x^6-x^4+x^4-1
=x^6-1
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问题中的2是平方
(x+1)(x-1)(x^2-x+1)(x^2+x+1)
=(x+1)(x-1)[(x^2+1)-x][(x^2+1)+x]
=(x^2-1)[(x^2+1)^2-x^2]
=(x^2-1)(x^4+x^2+1)
=x^4(x^2-1)+(x^2-1)(x^2+1)
=x^6-x^4+x^4-1
=x^6-1