3x^3+(2a+1)x^2+(a^2+2a-1)x+(a^2-1)求分解因式
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解决时间 2021-03-30 14:07
- 提问者网友：不爱我么
- 2021-03-30 02:48
两日之内
最佳答案
- 五星知识达人网友：有你哪都是故乡
- 2020-11-05 01:12
3x^3+(2a+1)x^2+(a^2+2a-1)x+(a^2-1)
=3[x^3+x^2]+[2ax^2+(a^2+2a-1)x+(a^2-1)]
=3x^2(x+1)+[2ax^2+2ax+(a^2-1)x+(a^2-1)]
=3x^2(x+1)+[2ax(x+1)+(a^2-1)(x+1)]
=3(x+1)(x^2+2ax+a^2-1)
=3(x+1)[x^2+(a+1)x+(a-1)x+a^2-1]
=3(x+1)[x(x+a+1)+(a-1)(x+a+1)]
=3(x+1)(x+a+1)(x+a-1)
=3x+3+3x+3a+3+3x+3a-3
=9x+6a+6
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=3[x^3+x^2]+[2ax^2+(a^2+2a-1)x+(a^2-1)]
=3x^2(x+1)+[2ax^2+2ax+(a^2-1)x+(a^2-1)]
=3x^2(x+1)+[2ax(x+1)+(a^2-1)(x+1)]
=3(x+1)(x^2+2ax+a^2-1)
=3(x+1)[x^2+(a+1)x+(a-1)x+a^2-1]
=3(x+1)[x(x+a+1)+(a-1)(x+a+1)]
=3(x+1)(x+a+1)(x+a-1)
=3x+3+3x+3a+3+3x+3a-3
=9x+6a+6
------------------------------------------------------------------------------------------------------------------------
祝您学习进步！
采纳是我前进的动力~
如果您觉得满意，可以点击“采纳为满意答案”哦！
全部回答
- 1楼网友：duile
- 2019-11-21 14:45
x^3+(2a+1)x^2+(a^2+2a-1)x+a^2-1
=x^2(x+1)+2ax(x+1)+a^2(x+1)-(x+1)
=(x+1)*(x^2+2ax+a^2-1)
=(x+1)〔(x+a)^2-a^2+a^2-1〕
=(x+a)(x+a-1)(x+a+1)
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