因式分解綜合專項練習76題

1、因式分解綜合專項練習76題（有答案）(7)-2xy-x2-y2,(1)9(a+b)2-4(a-b)2,22、2,22(2)(x+y)-4xy,(8)16(m-n)2-9(m+可2,(3)ax2-16ay2(9)4x2(x-y)+(y-x),(4)-2a3+12a2-18a(10)(a+1)(a2+2a1)+2(a+1)(5)x2-7x+10(11)a2(x-y)+b2(y-x)(6)a2-2ab+b2-12(12)xxyy213(13)-3a+12a(19)4ab2-4a2b-b3(14)a2(xy)-4a(y-x)+4(xy)(20)16(m-n)2-9(m+n2(15)(a+2)(a2)+

2、3a(21)x2(x-y)+(y-x)(16)x3-2x2+x(18)4x2-64(22)6m(m+D-4n(m+n(17)8(x22y2)-x(7x+y)+xy(23)x4-y4(24)-3a2+12ab-12b2.(32)4x3-8x2+4x(26)2x3-12x2y+18xy2(27)x2-2xy+y2-9(33)(x+y+z)2-(x-y-z)(28)ax2-16ay2/、/、2(34)(x-1)-上4(29)a3+ab2-2a2b(35)a2(x-y)-b2(x-y)(36)2x2-12x+18(30)x2y(m-n)-xy2(n-m)(38)x3y-x2y2-12xy3(44)2a

3、2b+4ab-2b(39)2x2-8xy+8y2;,、.4.224(45)16x8xy+y(46)a3-6a2-7a/5/222,22(40)(x+y)4xy.(41)(a-b)3-2(b-a)(47)(x2+x)2-(x+1)(42)3x3-12x2y+12xy2322(48)-4xy+28xy-2xy(50)(x2+1)2-4x(x2+1)+4x2(56)4(x-2)2-12222.(51)xy-x-4y+4xy2(57)(x+y)+4(x+y+1)(52)(a2+1)(a2+2)+【.4(58)2x(x3)-8(53)2,、2a(b+c)(59)x2+y2b22xy43223(60)3a

4、bc12abc+12abc,(54)(x-y)(x2-xy+y2)-xy(x-y)(67) (61)16(a-b)2-9(a+b)2,x(xy)y(yx)(62)3x(a-b)-6y(b-a)(68)3a2-12b2(63)a2+2a(b-c)+(b-c)2(69)m(a1)2m(a1)+(a1)(64)4ab2-4a2b-b3(70)(a-b)2+4ab(65)x3-2x2y+xy2(71)x2(a-b)+4(b-a)(66)x2-4y2-3x+6y(72)49(m+D2-25(n-m)2(73)(y-x)2-10x+10y+25(74)a(x-a)(x+y)2-b(x-a)2(x+y)4x

5、2y2+4xy3的(75)已知：xy=2,x=2y+1.求：x3y值.1,比較代數(shù)式(76)已知P=2W+4y+13,Q=頂-y2+6xP,Q的大小.因式分解綜合76題參考答案:=(xv)(a+b)(a-b);(1)9(a+b)2-4(a-b)2,(12)x2-xyJ_y2-1.4(a+b)-2(ab),=3(a+b)+2(a-b)3=(5a+b)(a+5b);22、2.22(2)(x+y)-4xy,/2222=(x+y+2xy)(x+y-2xy),=(x+y)2(x-y)2.(5)ax2-16ay2=a(x216y2)=a(x+4y)(x-4y);=(x-iy+1)(x-y-1).223(1

6、3)-3a+12a2.、=-3a(a-4)=-3a(a+2)(a2);-2a3+12a2-18a=-2a(a2-6a+9)2=-2a(a-3);(5)x2-7x+10=(x-2)(x-5);a2-2ab+b2-1=(a-b)2-1=(ab+1)(ab-1).(14)a2(x-y)-4a(y-x)+4(x-y)=(x-y)(a2+4a+4)2=(x-y)(a+2).(15)(a+2)(a-2)+3a=a2+3a-4=(a+4)(a-1)(16)x3-2x2+x=x(x2-2x+1)2=x(x1);=(x-y)(2x+1)(2x-1).(1)x3y-xy3-2xy-x2-y2,=-(2xy+x2+

7、y2),/、2=-(x+y);16(nrn)2-9(m+D2,=4(mn)+3(m+D4(mn)-3(m+©,=(7mn)(m7n);4x2(x-y)+(y-x),=4x2(x-y)-(x-y),=(x-y)(4x2-1),=xy(x2-y2)=xy(x+y)(x-y);(a+1)(a2+2a-1)+2(a+1)=(a+1)(a2+2a+1)3=(a+1)8(x22y2)-x(7x+y)+xy=8x2-16y2-7x2-xy+xy=x2-16y2=(x+4y)(x4y).(17) 4x2-64，2一、=4(x-16)=4(x+4)(x4);4ab2-4a2b-b3=-b(4a2-4a

8、b+b2)2=-b(2a-b);16(m-n)2-9(m+Q2=4(m-n)+3(m+D4(m-n)-3(m+n=(7葉n)(m7n);(22)x2(x-y)+(y-x)=(xy)(x+1)(x1).(22)6m(m+D-4n(m+rj)=2(m+n)(3m2n);(7) a2(x-y)+b2(y-x)=a2(x-y)-b2(x-y)=(x-y)(a2-b2)(23)x4-y4=(x2+y2)(x2y2)=(x2+y2)(x+y)(x-y);-,一、2=2(x3);(24) -3a2+12ab-12b2.=-3(a2-4ab+4b2)一，一、2=-3(a-2b)4a2-1=(2a+1)(2a-

9、1);2x3-12x2y+18xy2=2x(x2-6xy+9y2)2=2x(x-3y);(28)x22xy+y2-9=(x-y)2-32=(xy+3)(xy-3).(37)2x3-18x-，2一、=2x(x-9)=2x(x+3)(x-3);,、3223(38)xy-xy-12xy=yx(x2-xy-12y2)=xy(x4y)(x+3y).(39)2x2-8xy+8y2;=2(x?-4xy+4y之)-,一、2=2(x2y);(28)ax2-16ay2=a(x16y)=2(x+4y)(x4y);22、2.22(40)(x+y)-4xy./2222=(x+y+2xy)(x+y-2xy)=(x+y)2

10、(x-y)2.(y-x)1)；(31) (29)a3+ab2-2a2b=a(a2+b2-2ab)2=a(a-b);(31)x2y(m-n)-xy2(n-m)=xy(mn)(x+y);a2+2ab+b2-9，、2一=(a+b)-9=(a+b+3)(a+b-3).4x3-8x2+4x=4x(x2-2x+1)2=4x(x1);(41)(a-b)3-2(b-a)2=(a-b)2(a-b-2)；(42)3x3-12x2y+12xy2=3x(x2-4xy+4y2)2=3x(x2y)(3a-b)(x-y)+(a+3b)=(x-y)(3a-b)-(a+3b)=(x-y)(2a4b)=2(x-y)(a-2b).

11、(43) 2a2b+4ab-2b=2b(a2+2a-(33)(x+y+z)2-(x-y-z)2=(x+y+z)+(x-y-z)(x+y+z)(xy-z)=4x(y+z).4224(44) 16x-8xy+y=(4x2-y2)2=(2x+y)2(2x-y)2;(47)a3-6a2-7a=a(a2-6a-7)=a(a7)a+1);2-(x+1)2(x2+x-x-1)=(x+1)=(x+1)(49)-=-2xy(37)a2(x-y)-b2(x-y)=(x-y)(a2-b2)=(x-y)(a+b)(a-b).(36)2x2-12x+18=2(x2-6x+9)(47)(x2+x)=(x2+x+x+1)2

12、(x+1)(x-1)3(x-1).,3224xy+28xy-2xy(2x2y-14x+1);(49)a3-4ab2=a(a2-4b2)=a(a+2b)(a2b);(62)3x(a-b)-6y(b-a)=3(a-b)(x+2y);(50)(x2+1)=(x2+1-2x)=(xT)42-4x(x2+1)+4x22(63)a2+2a(b-c)+(b-c)22=(a+b-c);2-4y2+4xy2(x-2y)(51)x2y2-x/、2=(xy)=(xy+x-2y)(xy-x+2y)(52) (a+1)(a+2)+.=a4+3a2+=3住22,.、2a-(b+c)=a+(b+c)a-(b+c)=(a+b

13、+c)(a-b-c);(x-y)(x2-xy+y2)-xy(x-y)=(x-y)(x2-2xy+y2),、3=(x-y);(53) x2+7x-18.=(x2)(x+9).4(x-2)2-1=2(x-2)+12(x2)-1=(2x-3)(2x-5);,、2,.、(x+y)+4(x+y+1)2=(x+y+2);2x(x-3)-8=4x2-6x-8=2(x-4)(x+1);x2+y2b2-2xy=(x-y)2-b2=(xy+b)(xyb).432233abc-12abc+12abc,=3a2bc(a2-4ab+4b2),=3a2bc(a-2b)2;16(a-b)2-9(a+b)2,=4(a-b)+

14、3(a+b)4(a-b)-3(a+b),=(7a-b)(a-7b).(1)4x2-64=4(x2-16)=4(x+4)(x4);4ab2-4a2b-b3=-b(-4ab+4a2+b2)，一、2=-b(2a-b)x32x2y+xy2=x(x2-2xy+y2)2=x(x-y);x2-4y2-3x+6y=(x+2y)(x-2y)-3(x-2y)=(x2y)(x+2y3)x(x-y)-y(y-x)=(x-y)(x+y);3a2-12b2=3(a2-4b2)=3(a+2b)(a-2b);2m(a-1)-2m(a-1)+(a-1)2=(a1)(m2m+12=(a1)(m1)；(a-b)2+4ab=a2-2ab+b2+4ab2=(a+b).x2(ab)+4(ba)=x2(a-b)-4(a-b)2.、=(ab)(x4)=(ab)(x+2)(x2);49(m+D2-25(n-m)2=7(m+D+5(ng7(m+可-5(nm=(7m+7n+5z5n)(7m+7n5n+5ni)=(2m+12n)(12m+2rj)=4(m+6©(6m+©(y-x)2-10x+10y+25=(x-y)2-10(x-y)+252=(xy-5);22(64) a(x-a)(x+y)-b(