9道因式分解题

1.(x+y)^3+2xy(1-x-y)-12.x^3+x^2-2004*2005x3.(x^2-x-6)(x^2+3x-4)+244.x^6+15x^3y+50y^25... 1.(x+y)^3+2xy(1-x-y)-1
2.x^3+x^2-2004*2005x
3.(x^2-x-6)(x^2+3x-4)+24
4.x^6+15x^3y+50y^2
5.(x^2+4x+6)+(x^2+6x+6)+x^2
6.(x-3)(x+4)(x-5)(x+6)+80
7.x^3-7x+6
8.x^4+y^4+(x+y)^4
9.xy(xy+1)+(xy+3)-2(x+y+1/2)-(x+y-1)^2
展开
紫罗兰爱橄榄树
2010-08-12 · TA获得超过9103个赞
知道小有建树答主
回答量:576
采纳率:0%
帮助的人:1321万
展开全部
1)(x+y)^3+2xy(1-x-y)-1
立方差公式:a³-b³=(a-b)(a²+ab+b²)
(x+y)^3+2xy(1-x-y)-1
=[(x+y)³-1]-2xy(x+y-1)
=(x+y-1)[(x+y)²+(x+y)+1]- 2xy(x+y-1)
=(x+y-1)(x²+y²+x+y+1)

2)x^3+x^2-2004*2005x
=x(x²+x-2004×2005)
=x(x+2005)(x-2004)

3)(x^2-x-6)(x^2+3x-4)+24
=(x-3)(x+2)(x+4)(x-1)+24
=[(x-3)(x+4)][(x+2)(x-1)]+24
=(x²+x-12)(x²+x-2)+24
=[(x²+x)-12][(x²+x)-2]+24
=(x²+x)²-14(x²+x)+24+24
=(x²+x)²-14(x²+x)+48
=(x²+x-6)(x²+x-8)
=(x+3)(x-2)(x²+x-8)

4)x^6+15x^3y+50y^2
设x³=a,
原式
=a²+15ay+50y²
=(a+10y)(a+5y)
再代回去
=(x³+10y)(x³+5y)

5)(x^2+4x+6)+(x^2+6x+6)+x^2
设x²+5x+6=a
原式
=(a-x)(a+x)+x²
=a²
=(x²+5x+6)²
=(x+3)²(x+2)

6)(x-3)(x+4)(x-5)(x+6)+80
(x-3)(x+4)(x-5)(x+6)+80
=(x-3)(x+4)(x-5)(x+6)+80
=(x²-x-12)(x²-x-30)+80
=[(x²-x)-12][(x²-x)-30]+80
=(x²-x)²-42(x²-x)+360+80
=(x²-x)²-42(x²-x)+440
=(x²-x-20)(x²-x-22)
=(x-5)(x+4)(x²-x-22)

7)x^3-7x+6
=x³-x²+x²-x-6x+6
=(x³-x²)+(x²-x)-(6x-6)
=x²(x-1)+x(x-1)-6(x-1)
=(x-1)(x²+x-6)
=(x-1)(x+3)(x-2)

8)x^4+y^4+(x+y)^4
=(x²+y²)²-2x²y²+(x+y)^4
=[(x+y)²-2xy]²-2x²y²+(x+y)^4
=(x+y)^4-4xy(x+y)²+4x²y²-2x²y²+(x+y)^4
=2(x+y)^4-4xy(x+y)²+2x²y²
=2【[(x+y)²]²-2xy(x+y)²+(xy)²】
=2[(x+y)²-xy]²
=2(x²+xy+y²)²

9)xy(xy+1)+(xy+3)-2(x+y+1/2)-(x+y-1)^2
=x²y²+xy+xy+3-2(x+y)-1-[(x+y)²-2(x+y)+1]
=[x²y²+2xy+1]-2(x+y)+1-(x+y)²+2(x+y)-1
=(xy+1)²-(x+y)²
=(xy-x-y+1)(xy+x+y+1)
=[x(y-1)-(y-1)][y(x+1)+(y+1)]
=(x-1)(x+1)(y+1)(y-1)

【希望对你有帮助】
毅丝托洛夫斯基
2010-08-12 · TA获得超过1.3万个赞
知道大有可为答主
回答量:1958
采纳率:0%
帮助的人:3116万
展开全部
1.(x+y)^3+2xy(1-x-y)-1
=(x+y)³-1-2xy(x+y-1)
=(x+y-1)[(x+y)²+x+y+1]-2xy(x+y-1)
=(x+y-1)[(x+y)²+x+y+1-2xy]
=(x+y-1)(x²+x+y+y²+1)

2.x^3+x^2-2004*2005x
=x³-2004x²+2005x²-2004*2005x
=x²(x-2004)+2005x(x-2004)
=(x²+2005x)(x-2004)
=x(x+2005)(x-2004)

3.(x^2-x-6)(x^2+3x-4)+24
=(x+2)(x-3)(x-1)(x+4)+24(这里注意组合 x-3 x+4 和 x+2 x-1)
=(x²+x-12)(x²+x-2)+24(这里将x²+x 看成一个整体)
=(x²+x)²-14(x²+x)+48
=(x²+x-6)(x²+x-8)
=(x-2)(x+3)(x²+x-8)

4.x^6+15x^3y+50y^2
=x^6+10x^3y+5x^3y+50y^2
=x^3(x^3+10y)+5y(x^3+10y)
=(x^3+5y)(x^3+10y)

5.(x^2+4x+6)+(x^2+6x+6)+x^2
(这题符号是不是有问题)?

6.(x-3)(x+4)(x-5)(x+6)+80
同第三题注意组合
=(x²+x-12)(x²+x-30)+80
=(x²+x)²-42(x²+x)+360+80
=(x²+x-20)(x²+x-22)
=(x+5)(x-4)(x²+x-22)

7.x^3-7x+6
=x^3-1-7x+7
=(x-1)(x²+x+1)-7(x-1)
=(x-1)(x²+x-6)
=(x-1)(x-2)(x+3)
好累最后自己尝试吧 加油!

8.x^4+y^4+(x+y)^4
9.xy(xy+1)+(xy+3)-2(x+y+1/2)-(x+y-1)^2
已赞过 已踩过<
你对这个回答的评价是?
评论 收起
推荐律师服务: 若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询

为你推荐:

下载百度知道APP,抢鲜体验
使用百度知道APP,立即抢鲜体验。你的手机镜头里或许有别人想知道的答案。
扫描二维码下载
×

类别

我们会通过消息、邮箱等方式尽快将举报结果通知您。

说明

0/200

提交
取消

辅 助

模 式