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1、因式分解高一难题集锦说明： 本课件不同于其他因式分解系列课件。 本课件在因式分解基础之上逐步提升一层。 包含各类因式分解难题，错题。 请讲解完因式分解基础部分再使用本课件。 感谢！Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-
2、2011 Aspose Pty Ltd.试着因式分解下列难题！bc(b+c)+ca(c-a)-ab(a+b)n提示：n运用加减因式来完成此 题Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd
3、.解法（仔细思考后再对照答案 ）n=bc(c-a+a+b)+ca(c-a)-ab(a+b) =bc(c-a)+bc(a+b)+ca(c-a)-ab(a+b) =bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b) =(bc+ca)(c-a)+(bc-ab)(a+b) =c(c-a)(b+a)+b(a+b)(c-a) =(c+b)(c-a)(a+b)n当遇到实在无法解出的题目，可以尝试用这个方法！Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.
4、Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.试着因式分解下列难题！(x2+x+1)(x2+x+2)-12n提示n尝试换元解决此题Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides f
5、or .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.解法（仔细思考后再对照答案 ）n可以令y=x2+x,则 原式=(y+1)(y+2)-12 =y2+3y+2-12=y2+3y-10 =(y+5)(y-2) =(x2+x+5)(x2+x-2) =(x2+x+5)(x+2)(x-1)Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client
6、 Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.试着因式分解下列难题！(1+y)2-2x2(1+y2)+x4(1-y)2 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Asp
7、ose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.解法（仔细思考后再对照答案 ）n原式=(1+y)2+2(1+y)x2(1+y)+x4(1- y)2-2(1+y)x2(1-y)-2x2(1+y2) =(1+y)+x2(1-y)2-2(1+y)x2(1-y)- 2x2(1+y2) =(1+y)+x2(1-y)2-(2x)2 =(1+y)+x2(1-y)+2x(1+y)+x2(1-y)- 2x =(x2-x2y+2
8、x+y+1)(x2-x2y-2x+y+1) =(x+1)2-y(x2-1)(x-1)2-y(x2-1) =(x+1)(x+1-xy+y)(x-1)(x-1-xy-y) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 A
9、spose Pty Ltd.试着因式分解下列难题！nx5+3x4y-5x3y2+4xy4+12y5 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.解法（仔细思考后再对照答案 ）n原式=(
10、x5+3x4y)- (5x3y2+15x2y3)+(4xy4+12y5 ) =x4(x+3y)- 5x2y2(x+3y)+4y4(x+3y) =(x+3y)(x4-5x2y2+4y4) =(x+3y)(x2-4y2)(x2-y2) =(x+3y)(x+y)(x-y)(x+2y)(x-2y) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2
11、.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.试着因式分解下列难题！n1.(2a-b)+8ab 2.y-2y-x+1 3.x-xy+yz-xz 4.6x+5x-4 5.2a-7ab+6bn看你需要多少时间解完以上小题。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Cl
12、ient Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.解法（仔细思考后再对照答案 ）n答案：1.(2a-b)+8ab=(2a+b) 2.y-2y-x+1=(y-1)-x=(y-1-x)(y-1+x) 3.x-xy+yz-xz =x(x-y)-z(x-y)=(x- z)(x-y) 4.6x+5x-4 =(2x-1)(3x+4) 5.2a-7ab+6b=(2a-3b)(a-2b)Evaluation only.Evaluation only. Created with
13、Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.n6.(x-2x)+2(x-2x)+1 7.(x-2x)-14(x-2x)-15 8.x(x-y)+(y-x) 9.169(a+b)-121(a-b) 10.(x-3)(x-5)+1 试着因式分解下列难题！Evaluation on
14、ly.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.解法（仔细思考后再对照答案 ）n6.(x-2x)+2(x-2x)+1 =(x-2x+1)=(x-1)4 7.(x-2x)-14(x-2x)-15 =(x-2x-15)
15、(x- 2x+1)=(x+3)(x-5)(x-1) 8.x(x-y)+(y-x) =(x-1)(x-y)=(x+1)(x-1)(x-y) 9.169(a+b)-121(a-b) =(14a+14b-11a+11b)(14a+14b+11a-11b) =(3a+25b)(25a+3b) 10.(x-3)(x-5)+1 =(x-3)-2(x-3)+1 =(x-3- 1)=(x-4) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with
16、Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.n因式分解9x230x25n因式分解20x29x20n因式分解12x229x15n因式分解36x239x9n因式分解21x231x22n用十字相乘解决以上问题！试着因式分解下列难题！Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5
