(x+1)(x-1)(x²-x+1)(x²+x+1)怎么解
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解决时间 2021-02-15 19:46
- 提问者网友：温柔港
- 2021-02-15 04:55
(x+1)(x-1)(x²-x+1)(x²+x+1)怎么解
最佳答案
- 五星知识达人网友：佘樂
- 2021-02-15 06:04
(x+1)(x-1)(x^2-x+1)(x^2+x+1)
=(x²-1)[(x²+1)²-x²]
=x²(x²+1)²-x^4-(x²+1)²+x²
=x^6+2x^4+x²-x^4-x^4-2x²-1+x²
=x^6-1
=(x²-1)[(x²+1)²-x²]
=x²(x²+1)²-x^4-(x²+1)²+x²
=x^6+2x^4+x²-x^4-x^4-2x²-1+x²
=x^6-1
全部回答
- 1楼网友：山河有幸埋战骨
- 2021-02-15 07:14
(x+1)(x-1)(x²-x+1)(x²+x+1)
=((x+1)(x²-x+1))((x-1)(x²+x+1))
=(x³-x²+x+x²-x+1)(x³+x²+x-x²-x-1)
=(x³+1)(x³-1)
=(x^6)-1
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