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1、因式分解综合专项练习76题（有答案）(7)-2xy-x2-y(1)9(a+b)2-4(a-b)2,(2)(x2+y2)2-4x2y2(8)16(m-n)2-9(m+n)2,(3)ax2-16ay2(9)4x2(x-y)+(y-x),(4)-2a3+12a2-18a(10)(a+1)(a2+2a-1)+2(a+1)(5)x2-7x+10(11)a2(x-y)+b2(y-x)(20)16(m-n)~-9(m+n)2(14)a“(x-y)-4a(y-x)+4(x-y)(15)(a+2)(a-2)+3a(21)x2(x-y)+(y-x)(16)x3-2x2+x(22)6m(m+n)-4n(m+n)(
2、17)8(x2-2y2)-x(7x+y)+xy(23)x4-y1(18)4/-64(24)-3a2+12ab-12b(26)2x3-12x2y+18xy2(32)4x3-8x2+4x(27)x2-2xy+y2-9(33)(x+y+z)2-(x-y-z)(28)ax2-16ay2(34)(x-1)24(29)a3+ab2-2ab(35)a2(x-y)-b「(x-y)(36)2x2-12x+1822x(30)x了(m-n)-xy^(n-m)(38)x'y-x了$-12xy3(44)2a2b+4ab-2b(39)2x2-8xy+8y2；(45)16xl-8x2y2+y4(46)a3-6a2-7a(
3、40)(x2+y2)2-4x2y2(41)(a-b)3-2(b-a)(47)(x~+x)--(x+1)(42)3x3-12x2y+12xy2(48)-4x3y2+28x2y-2xy(50)(x2+l)2-4x(x2+l)+4x2(56)4(x-2)1(51)x2y2-x2-4y2+4xy(57)(x+y)2+4(x+y+1)(52)d+1)(H)+寺(58)2x(x-3)-8(53)a2-(b+c)(59)x2+y2-b~-2xy22(54)(x-y)(x—xy+yJ-xy(x-y)(60)3a*bc-12a：Vc+12ab3c,(68)3a2-12b2(62)3x(a-b)-6y(b-a)(
4、63)a2+2a(b-c)+(b-c)(69)m(a-1)-2m(a-1)+(a-1)(64)4ab2-4a2b-b3(70)(a-b)2+4ab(65)x-2x^y+xy2(71)x2(a-b)+4(b-a)(66)x2-4y2-3x+6y(72)49(m+n)—25(n-m)(73)(y・x)10x+10y+25(74)a(x-a)(x+y)(x-a)2(x+y)(75)已知：xy=2,x=2y+l.求：x3y-4x2y2+4xy3的值.(76)己知P=2x2+4y+13,Q=x2-y2+6x-1,比较代数式P,Q的大小.因式分解综合76题参考答案:(1)9(a+b)—4(a・b)2,二[
5、3(a+b)+2(a・b)][3(a+b)・2(a・b)],=(5a+b)(a+5b)；(2)(x2+y2)2-4x2y2,=(x'+『+2xy)(x2+y2-2xy),=(x+y)2(x-y)1(5)ax2-16ay2=a(x"-16y2)二a(x+4y)(x-4y)；(6)-2a3+12a2-18a=-2a.(a2-6a+9)=-2a(a-3)2；(5)x2・7x+10=(x-2)(x・5)；(7)a-2ab+b2-1=(a-b)2-1=(a-b+1)(a-b-1).(7)-2xy-x2-y2,=-(2xy+x2+y2)，=-(x+y)2；(8)16(m・n)2-9(m+n)2,=[4(m
6、-n)+3(m+n)][4(m-n)-3(m+n)],=(7m-n)(m-7n)；(9)4x2(x-y)+(y-x),=4x"(x-y)-(x-y),=(x-y)(4x2-1),=(x-y)(2x+l)(2x-1).(1)x3y-xy3=xy(x2-『)=xy(x+y)(x-y)；(10)(a+1)(a2+2a-1)+2(a+1)=(a+1)(a2+2a+l)二(a+1)3(11)a2(x-y)+b2(y-x)=a2(x-y)-b'(x-y)=(x-y)(a"-b2)=(x-y)(a+b)(a-b)；(12)x2-xy+丄y，-1.4=(x-丄y)2-12=(x-丄y+1)(x-丄y-1).2
7、'2'(13)-3『+12a=-3a(a2-4)--3a(a+2)(a-2)；(14)a"(x-y)-4a(y-x)+4(x-y)=(x-y)(a2+4a+4)=(x-y)(a+2)2.(15)(a+2)(a-2)+3a=a2+3a-4=(a+4)(a-1)(16)x3-2x2+x=x(x2-2x+l)=x(x-1)2;(17)8(x2-2y2)-x(7x+y)+xy222=8x-16y-7x-x
