(677)因式分解綜合專(zhuān)項(xiàng)練習(xí)76題(有答案)

1、因式分解綜合專(zhuān)項(xiàng)練習(xí)76題（有答案）2 2(7)- 2xy - x - y ,2 2(1) 9 (a+b)- 4 (a - b),z 、 z 2 2 2 2 2(2) (x +y )- 4x y ,2 2(8) 16 (m n) 9 (m+r),/ 、 2 2(3) ax - 16ay2(9) 4x (x- y) + (y- x),32(4)- 2a +12a - 18a2(10) (a+1) ( a +2a- 1) +2 (a+1)2(5) x - 7x+1029(11) a (x- y) +b (y - x)2 2(6) a - 2ab+b - 1(12) x2 - xy+ y2- 1 .

2、4(13)-3a3+12a(19)4ab2 - 4a2b - b3(18)4x - 64(24)(14)2a (x - y)- 4a (y- x) +4 ( x- y)(20)2 216 (m- r) 9 ( m+r)(15)(a+2) (a- 2) +3a(21)x2 (x - y) + (y- x )(16)3 小2x - 2x +x(22)6m (m+n - 4n (m+r)(17)2 28 ( x - 2y ) - x (7x+y) +xy(23)2 2-3a+12ab - 12b .(25)4a2-1(31)(26)2x3-2 212x y+18xy(32)(27)(28)(29)2

3、 2a +2ab+b - 9,32,4x - 8x +4x2x - 2xy+y - 92 2ax - 16ay3, 2 小 2,a +ab - 2a b2 2x y (m- n) xy (n - m)(33)(34)(35)(36)2 2(x+y+z )-( x - y - z)(x- 1) 2-22x 12x+18(31)(37)2x3-18x(43)(3a-b) (x y) + (a+3b) (y x)(43)(48)(38)2 2“3x y - 12xy(44)22a b+4ab - 2b(39)2x2-28xy+8y ;(45)416x 8x2 2 4y +y(40)/ 2 2、 2

4、,22(x +y )- 4x y .(46)32a - 6a -7a(41)32(a - b)- 2 (b - a)(47)(x2+x) 2-(x+1) 2c 3“2“23x - 12x y+12xy32“2小-4x y +28x y - 2xy(49)a3 4ab2(55)x +7x 18.2(55)(60)(50)2 2 2 2(x +1) 4x (x +1) +4x(56)24 (x 2) 1(51)2 2 2 2x y x 4y +4xy(57)2(x+y) +4 (x+y+1)(52)(a2+1) (a2+2) +_4(58)2x (x 3) 8(53)2 2a ( b+e)(59)

5、22,2小x +y b 2xy2 2(x y) (x xy+y ) xy (x y)43 22 33a be 12a b c+12a b c,(61)162(a b) 9(a+b) 2,(67)x (x - y) y ( y x)(62)3x(a b) 6y(b a)(68)2 23a 12b(63)2a +2a ( b c) +(b-c) 2(69)2m (a 1) 2m(a 1) + (a1)(64)4ab2 4a2b b3(70)2(a b) +4ab(65)322x 2x y+xy(71)2x (a b) +4 (b a)2 2x 4y 3x+6y2 249 ( m+n 25 ( n

6、m)(67)(72)do.dTX9+mo g+A寸+0d 呂 )赳 brAX寸+AX 寸Ax 堿 L+ACXIHX CXIUAXm*m(9卜) G o o GgCXI+AOL+XOL J (XA)o卜因式分解綜合76題參考答案:2 2(12) x - xy+ y - 1 .429(1) 9 (a+b) - 4 (a - b),=3(a+b) +2 (a - b) 3(a+b) - 2=(5a+b) (a+5b);(a - b),=(x-_y+1) (x-_y - 1).2 2，亠、，2 2、 2 2 2(2) (x +y )- 4x y ,2 2 2 2(x +y +2xy) (x +y -

7、2xy),2 2(x+y)(x - y).(13)=-3a=-3a3-3a +12a(a2-4)(a+2) ( a- 2);29(5) ax - 16ay29=a (x - 16y )=a (x+4y) (x - 4y);2a (x- y) - 4a ( y - x) +4 (x - y )2(x - y) (a +4a+4 )2(x- y) (a+2).(14)32(6)- 2a +12a - 18a2=-2a (a - 6a+9)2=-2a (a- 3);(15) (a+2) ( a- 2) +3a2=a +3a - 4=(a+4) (a - 1)2(5) x - 7x+10= (x-2

8、) (x - 5);2 2(7) a - 2ab+b - 12=(a-b)- 1=(a- b+1) (a- b- 1)./、32(16) x - 2x +x2=x (x - 2x+1)=x (x - 1) 2;2 2(7)- 2xy - x - y ,2 2=-(2xy+x +y ),=-(x+y) 2;2 2(8) 16 ( m- n) - 9 (m+r),=4 (m-門(mén))+3 ( m+r) 4 (m-門(mén))-3=(7m-門(mén))(m- 7門(mén))；(m+r),2(9 ) 4x (x- y) + (y - x),2 =4x ( x- y) -( x - y),2 =(x - y) (4x - 1),3

9、=(x - y) (2x+1) (2x- 1) .(1) x y2 2=xy (x - y )=xy (x+y) (x- y);3-xy2 2(17) 8 (x - 2y )- x (7x+y) +xy2 2 2=8x - 16y - 7x - xy+xy2 2=x - 16y=(x+4y) (x - 4y).2(18) 4x - 642=4 (x - 16)=4 (x+4) (x - 4);223(19) 4ab - 4a b- bz 2 2、=-b (4a - 4ab+b )2=-b (2a- b );(20) 16 ( m- r - 9 ( m+r)=4 (m-門(mén))+3 (m+r) 4

10、(m-門(mén))-3 (m+r)=(7m-門(mén))(m- 7門(mén))；2(22 ) x (x - y) + (y- x )=(x - y) (x+1) (x - 1).2(10 ) (a+1) (a +2a- 1) +2 ( a+1)2=(a+1) (a +2a+1)=(a+1) 3(22) 6m ( m+r) - 4n ( m+r)=2 ( m+r) (3m 2n);2+b (y - x)(x-y)2(11) a (x- y)2 2=a (x - y) - b (29=(x - y) (a - b )=(x - y) (a+b) ( a- b);44(23) x - y=(x +y ) (x - y )2

11、 2=(x +y ) (x+y) (x - y);2 2(24)- 3a+12ab - 12b .2 2=-3 (a - 4ab+4b )2=-3 (a - 2b)2(25) 4a - 1=(2a+1) (2a- 1);3 2 2(26) 2x - 12x y+18xy2 2=2x (x - 6xy+9y )2=2x (x- 3y);2 2(28) x - 2xy+y - 92 2=(x - y)- 3=(x - y+3) (x - y - 3).32 23(38) x y - x y - 12xy2 2=yx (x - xy - 12y )=xy (x - 4y) (x+3y).2 2(39

12、) 2x - 8xy+8y ;2 2=2 (x - 4xy+4y )2=2 (x-2y);/ 、 2 2(28) ax - 16ay2 2=a (x - 16y )=2 (x+4y) (x - 4y);2 2、 2 ,22(40) (x +y )- 4x y ./ 2 2 、/ 2 2 、 =(x +y +2xy) (x +y - 2xy)2 2=(x+y)(x- y).3,22(29) a +ab - 2a b2 2=a (a +b - 2ab)=a (a - b) 2;3(41) (a - b)- 2 (b- a)2=(a- b)(a - b - 2)；2 2(31) x y (m- n)

13、- xy (n- m)3 2 2(42) 3x - 12x y+12xy2 2=3x (x - 4xy+4y )2=3x (x- 2y)=xy ( m- n) (x+y);(43) (3a - b) (x - y) + (a+3b) (yx)2 2(31) a +2ab+b - 92=(a+b)- 9=(a+b+3) (a+b - 3).32(32) 4x - 8x +4x2=4x (x - 2x+1 )2=4x (x - 1);=(x - y) ( 3a- b)-( a+3b)=(x - y) (2a - 4b)=2 (x - y) (a - 2b).2 2(44) 2a b+4ab - 2

14、b=2b (a +2a - 1);29(33) (x+y+z) -( x - y- z)=(x+y+z) + (x - y - z) (x+y+z)-( x- y- z)=4x (y+z).(x - 1) 2 -：(36)=(x - 1+ ) (x - 1 -)2 2=(x - 2)( x -2 242 24(45) 16x - 8x y +y2 2 2=(4x - y )2 2=(2x+y)(2x- y);/、32(47) a - 6a - 7a2=a (a - 6a- 7)=a (a- 7) a+1);29(37) a (x - y)- b (x - y)29=(x - y) (a - b

15、 )=(x - y) (a+b) (a- b).2(36) 2x - 12x+182=2 (x - 6x+9)2=2 (x - 3);2 2 2(47) (x +x)-( x+1)2 2=(x +x+x+1) (x +x - x - 1)2=(x+1)(x+1) (x- 1 )=(x+1) 3 (x - 1).3 2 2(49)- 4x y +28x y - 2xy2=-2xy (2x y- 14x+1);(49) a3 - 4ab2=a (a - 4b )=a (a+2b) (a - 2b);3(37) 2x - 18x2=2x (x - 9)=2x (x+3) (x - 3);2(50)

16、(x +1)2=(x+1 - 2x)=(x- 1) 42 , 2 、-4x (x +1)+4x2 2 2 2(51) x y - x - 4y +4xy229=(xy)-( x - 2y )=(xy+x - 2 y) (xy - x+2 y)(52 ) (a2+1) (a2+2 ) + .43(65) x - 2x y+xy2 2=x (x - 2xy+y )=x (x - y) 2;4=a +3a +4z 2 2=(a +22 2(53) a -( b+c)=a+(b+c ) a -( b+c)=(a+b+c) (a - b - c);2 2(54 ) (x - y) (x - xy+y )

17、 - xy (x - y)2 2=(x - y) (x - 2xy+y )=(x - y ) 3;2(55 ) x +7x- 18.=(x - 2) (x+9).29(66) x - 4y - 3x+6y=(x+2y) (x- 2y)- 3 (x- 2y)=(x- 2y) (x+2y - 3)(67) x (x - y)- y (y- x)=(x- y) (x+y);2 2(68) 3a - 12b29=3 (a - 4b )=3 (a+2b) (a - 2b);2(56 ) 4 ( x- 2)- 1=2 (x - 2 ) +12(x- 2) - 1=(2x - 3) (2x - 5);2(6

18、9) m (a- 1) - 2m ( a- 1) + (a- 1)2=(a- 1) (m - 2m+12=(a- 1) (m- 1 );2(57) (x+y)+4 (x+y+1)=(x+y+2) 2;(58) 2x (x - 3)- 8 =4x2 - 6x - 8=2 (x - 4) (x+1);2(70) (a - b) +4ab2 2=a - 2ab+b +4ab=(a+b) 2.2(71) x (a- b) +4 (b - a)2=x (a- b)- 4 (a - b)=(a- b)=(a- b)(x2- 4)(x+2) (x - 2);2 2 2(59 ) x+y - b - 2xy2 2=(x - y )- b=(x - y+b) (x - y - b)./、43 22 3(60 ) 3a bc - 12a b c+12a b c,2 2 2=3a bc (a - 4ab+4b ),29=3a bc (a- 2 b);(72) 49=7 ( m+n +5 (n m) 7 ( m+n) - 5 ( n- m) =(7m+7n+5n- 5m) (7m+7n 5n+5m)=(2m+12r) (12m+2n=4 ( m+6r) (6m+r);2 2(m+n - 25 ( n - m)29(61) 16 (a - b )- 9 (a+