因式分解 (x-1)^6-(x+1)^6
答案:2 悬赏:50 手机版
解决时间 2021-02-21 04:56
- 提问者网友：沦陷
- 2021-02-20 10:04
因式分解 (x-1)^6-(x+1)^6
最佳答案
- 五星知识达人网友：街头电车
- 2021-02-20 11:38
(x-1)^6-(x+1)^6
=[(x-1)^3-(x+1)^3][(x-1)^3+(x+1)^3]
=[(x-1)-(x+1)][(x-1)^2+(x-1)(x+1)+(x+1)^2][(x-1)+(x+1)][(x-1)^2-(x-1)(x+1)+(x+1)^2]
=(-2)*[(x-1)^2+(x-1)(x+1)+(x+1)^2]*(2x)*[(x-1)^2-(x-1)(x+1)+(x+1)^2]
=(-4x)*[(x-1)^2+(x-1)(x+1)+(x+1)^2][(x-1)^2-(x-1)(x+1)+(x+1)^2]
=(-4x)*[2x^2+2+(x-1)(x+1)][2x^2+2-(x-1)(x+1)]
=(-4x)*[2x^2+2+x^2-1][2x^2+2-(x^2-1)]
=(-4x)*[3x^2+1][x^2+3]
=-4x*(3x^2+1)(x^2+3)
=[(x-1)^3-(x+1)^3][(x-1)^3+(x+1)^3]
=[(x-1)-(x+1)][(x-1)^2+(x-1)(x+1)+(x+1)^2][(x-1)+(x+1)][(x-1)^2-(x-1)(x+1)+(x+1)^2]
=(-2)*[(x-1)^2+(x-1)(x+1)+(x+1)^2]*(2x)*[(x-1)^2-(x-1)(x+1)+(x+1)^2]
=(-4x)*[(x-1)^2+(x-1)(x+1)+(x+1)^2][(x-1)^2-(x-1)(x+1)+(x+1)^2]
=(-4x)*[2x^2+2+(x-1)(x+1)][2x^2+2-(x-1)(x+1)]
=(-4x)*[2x^2+2+x^2-1][2x^2+2-(x^2-1)]
=(-4x)*[3x^2+1][x^2+3]
=-4x*(3x^2+1)(x^2+3)
全部回答
- 1楼网友：酒醒三更
- 2021-02-20 13:16
(x+1)^6-(x-1)^6
=[(x+1)^3+(x-1)^3]*[(x+1)^3-(x-1)^3]
=[(x+1+x-1)(x^2+2x+1-(x^2-1)+x^2-2x+1)]*[(x+1-x+1)(x^2+2x+1+(x^2-1)+x^2-2x+1)]
=2x(x^2+3)*2(3x^2+1)
=4x(x^2+3)*(3x^2+1)
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