2020年初一數(shù)學(xué)(下)期中復(fù)習(xí)《因式分解》含答案

1、初一下數(shù)學(xué)期中復(fù)習(xí)因式分解因式分解-提公因式法1 .把下列各式分解因式:(2) 6a2b 15ab2+30 a2b2；(1) ax ay+ az ；(3) 10a (x y) 2 5b (y x);(4) x (a x) (a y) y (x a) (y a)3.2 .因式分解：(x+1 ) (x+3) 3(2019 秋？徐匯區(qū)校級(jí)期中)(x 3y) ( x -y) - ( - x-y) 2b-BI4 .因式分解：2m (a b) 3n (b a)5 . (2019 春？大豐區(qū)期末)因式分解：3x2 (x-2y)18x (x 2y)27 (2y x)2(1) x2 10x(2)8ax2+16

2、axy 8ay26 . (2018秋？如皋市期中)因式分解：6. (2017春？天寧區(qū)校級(jí)月考)因式分解：2x2-4x.8. (2017春？濱海縣期末)因式分解：(1) 3a (x y)5b (y x)(2) x6 x2y4.9. (2015春？新沂市期中)分解因式：3x(a-b)6y (b a)10. ( 2013春？常州期中)因式分解：3a2-6a2b+2 ab.11 . ( 2014春？常州期中)因式分解：6a (b-1) 2 2 (1b) 24(2) a2 (x y) b2 (x y)二.因式分解-運(yùn)用公式法12 .分解因式：(1) 16x2 8xy+y2；13 . (2019春？泰興

3、市期中)因式分解.6(1) 4x2 9y2(2)工2x2+2 xy+2 y214 .分解因式：(a2+1 ) 2 4a2.15 . (2018春？江寧區(qū)校級(jí)月考)分解因式.(2) ( x2 - x) 2 - ( x- 1)(1) ( m +1 ) ( m 9) +8 m15. (2018春？工業(yè)園區(qū)期末)分解因式：x4 2x2+1 .三.提公因式法與公式法的綜合運(yùn)用(2) 8a2 2b2 (3) 4+12 (x y) +9 (x y) 2(2) (a2+4)2 16a2(2) 3ax2+6 axy+3 ay2.20.分解因式：(1) 9ax2 ay2;(2) 2x3y+4 x2y2+2 xy3

4、.21 . ( 2020春？東臺(tái)市期中)因式分解 2x2 8 x3 2x2y+ xy2(x2+4 ) 2 16x2.17. ( 2020春？灌云縣期中)因式分解:(1) 2m (a b)3n (b a)18. (2019秋？崇川區(qū)校級(jí)期末)分解因式:(1) 4x2y 9y19. 因式分解(1) 4a2 9；7(2) x3 2x2+x.22. 因式分解：(1) x2 4;四.因式分解-分組分解法23. 分解因式：x2+y2+2xy-1.24. ( 2018春？玄武區(qū)校級(jí)期中)因式分解(2) (x+y) 2 4 (x+y 1)；(1) m2 (x 2) +m (2 x)8(3) (x2+y2) 2

5、 4x2y2；(4) x3+x2y xy2 y3.25. ( 2018秋？啟東市期中)分解因式(2) y3 6xy2+9 x2y(1) 16 a4(4) 9 a2+4 ab 4b2(3) (m + n) 2 4m (m+n) +4 m226. ( 2017秋？海安縣月考)因式分解:(1) a4 16(2) x2 2xy+y2 9 n2( m 2 ) + ( 2 m )(2) 4a (x y)2b (y x)27. ( 2017春？蘇州期中)分解因式:(1) 2a3 8a10(4) (x2+4 ) 2 16x2(4) 2xy x2+1y2.28. ( 2017春？江陰市校級(jí)月考)因式分解(1)

6、x3 4x(2)2a2+4 a 2(3) x2 5x 6(4) x2 4y2+ x+2 y.29. ( 2016春？鼓樓區(qū)校級(jí)期中)分解因式(1) 4x2 36;(2)4m3+8 m2+32 m；(4) (y2 1) 2 6 (y21) +9 ；30. ( 2016秋？啟東市校級(jí)月考)因式分解:(4) a2+ ac bc b2.(1) 3x 12 x3(2) a3 4ab211(3) ( 2x+y) 2( x+2 y) 2(4) a2 4a+4 c2.因式分解：(2) ( a+ b) 2 a2(3) 3a (x y) +9 (y x)31 . （ 2016秋？張家港市校級(jí)月考）（1） 3ax

7、3ay2(4) x4 18x2+81(5) x2 5x+6(6) a2+2 a+1b2.32. （ 2016春？江陰市校級(jí)月考）因式分解:(1) 3a512a4+9 a3(2) 3a2 6ab+3 b2 12c2.五.因式分解-十字相乘法等33. （ 2019春？常熟市期末）將下列各式分解因式：(3) a2 (x y) + b2 (y x)（1） x2 5x 6;（2） 8x2 8x+2 ;34. （ 2019春？相城區(qū)期中）將下列各式分解因式(1) 9x2 25(2) x4y4 8x2y2+1613(3) a2 (x y)b2 (x y)(4) x2 xy 6y235. ( 2019春？吳江

8、區(qū)期中)分解因式：(1) ax2 6ax+9 a(2) (m+1)(m 9) +8 m(3) a4+3 a2 436. ( 2019春？丹陽(yáng)市期中)分解因式(1) 6xz 9xy(2) 8a3 8a2+2 a(3) 2ax2 18 a3(4) x2 4x 1237. ( 2019春？常熟市期中)分解因式：(1) 3a2 6a+3 ；(2) a2 ab6b2；(3) 9a2 (2x y) + (y2x)38. ( 2019春？太倉(cāng)市期中)把下列各式分解因式(1) x4 81(3) 2x2y 8xy+8 y2039.分解因式：(a2+ a) 2 8 (a2+a) +12 .40. （ 2018春？

9、玄武區(qū)校級(jí)月考）分解下列因式(1) a2 (x y) +b2 (y x)(2) 16x4 8x2y2+y4(3) (x2+4 ) 2 16x2(4) 36 (a+b) 2 4 (a b) 2 x2 6x 1641 . （ 2018春？常熟市期末）將下列各式分解因式(1) 3x (a b)9y (b a);(2) a2 4a 12；(3) 81 x4 72x2y2+16 y442. （ 2018春？相城區(qū)期中）將下列各式分解因式:(1) 2ax2 8 a(2) x2 6xy+5 y2(4) a2 b2+2b 1(3) (2m n) 2 6n (2m n) +9 n2初一下期中復(fù)習(xí)因式分解答案因式

10、分解-提公因式法1. (1) ax ay+az = a (x y+z)； 6a2b 15ab2+30 a2b2=3ab (2a 5b+10 ab)；(3) 10a (x y) 2 5b (y x) = 10a (x y) 2+5 b (x y) = 5 (x y) 2a (x y) +b=5 (x y) (2ax 2ay+b)；(4) x (a x) (a y) y (x a) (y a) = x (a x) (a y) y (a x) (a y)=(a x) ( a y) (x y)2 . ( x+1 ) ( x+3 )3 = x2 +4 x+33 = x2+4 x= x (x+4 ),3.

11、y) 2=x22xy 3xy+*(x2+xyTy2)x2 ±xy 3xy+ -1Ly2 x2 xy Ay2, = gxy+Ly2, = y (x -y)4. 2m (a b)3n (b a) = 2m (a b) +3 n (a b) = ( a b) (2m+3n)5. 3x2 (x 2y)18x (x 2y)27 (2y x) = 3x2 (x 2y)18x (x 2y) +27 (x 2y)=3 (x 2y) ( x2 6x+9 ) = 3 (x 2y) (x-3) 2 .6. (1) x2 10x=x (x 10);(2) 8ax2+16 axy 8ay2= 8a (x2 2

12、xy+y2) = 8a (x y) 2.7. 2x2 4x=2x (x 2)8. (1)3a(x y)5b(y x)=(xy)(3a+5b)(2) x6x2y4=x2(x4y4) =x2(x2y2)(x2+y2)= x2(x y) (x+y) (x2+y2)9. 3x(a b)6y (b a) =3x(a b)+6y(a b)= 3 (a b) (x+2 y).10. 3a2 6a2b+2 ab = a (3a 6ab+2 b)11. . 6a (b1) 2 2 (1b) 2=2 (b1) 2 (3a - 1)因式分解-運(yùn)用公式法12. (1) 16x2 8xy+y2= (4x y) 2a2(

13、xy)b2(x y) = (xy)(a2b2) = (x y) (a+b) (a b)13 . ( 1) 4x2 9y2= ( 2x+3 y) ( 2x 3y)(2)x2+2 xy+2 y2(x2+4 xy+4 y2)(x+2 y) 214.(a2+1) 24a2.= (a2+1+2 a) (a2+12a)= (a+1) 2 (a 1) 215 . ( 1) ( m+1 ) (m 9) +8 m =m2 8m 9+8 m=m2 9=(m+3) (m 3)；(x2 x) 2 (x1) 2 = (x2 x+x 1) (x2 x x+1 ) = (x+1 ) (x 1) (x 1)2=(x+1 )

14、( x - 1 ) 3.16 . x4 2x2+1 = (x2 1) 2= (x+1 ) 2 (x 1) 2.三.提公因式法與公式法的綜合運(yùn)用17. (1) 2m(ab)3n(ba) =2m (ab) +3 n(ab)=(a b) (2m+3n)(2) 8a22b2=2 (4a2b2)=2 (2a+b)(2a b)(3) 4+12(xy) +9 (x y) 2 =2+3 (xy) 2=(2+3 x3y)218 .( 1)4x2y9y = y (4x29) = y (2x+3 ) ( 2x3)(2) (a2+4) 2 16a2=(a2+4 4a) (a2+4+4 a) = ( a+2 ) 2 (

15、a 2) 219. (1) 4a2 9= (2a+3) (2a 3) 3ax2+6 axy+3 ay2 = 3a (x2+2 xy+y2) =3a(x+y) 220. (1) 9ax2 ay2= a (9x2 y2) = a (3x+y) (3x y)(2) 2x3y+4 x2y2+2 xy3 = 2xy (x2+2xy+y2) = 2xy (x+y) 221 .2x2 8=2 (x2 4) = 2 (x 2) ( x+2 )x3 2x2y+xy2r (x2 2xy+y2) =x (x y) 2(x2+4 ) 2 16x2= ( x2+4 x+4 ) (x2 4x+4) = (x+2) 2 (

16、x 2) 222 . ( 1 ) x2 4= (x+2 ) (x-2);(2) x3 2x2 +x=x (x2 2x+1 ) = x (x 1 ) 2.四.因式分解-分組分解法23 . x2+ y2+2 xy 1 = (x+y) 21= (x+y 1) (x+y+1).24. (1)m2(x2)+ m (2 x) = m2(x 2) m(x2)= (x-2)(m2m)= m (x-2)(m1)；(x+y) 24 (x+y 1) = (x+y)2 4 (x+y) +4 = (x+y 2)2；(3) (x2+y2)2 4x2y2 = (x2+y2+2xy) (x2+y2 2xy) = (x+y)

17、2(xy) 2；(4) x3+ x2yxy2y3 = x2(x+y)y2(x+y)= (x+y)(x2y2)= (x+y)2(xy).25. (1) 16 a4= (4+a2)(4 a2) = (4+a2) (2+a) (2 a)(2) y3 6xy2+9 x2y = y (y2 6xy+9x2) = y (y 3x) 2(3) (m + n) 2 4m (m+n) +4 m2= (m + n 2m) 2= (n m) 2(4) 9 a2+4ab 4b2=9(a 2b) 2= (3 a+2b) (3+a 2b)26. ( 1)a4 16= (a2+4) (a24) = (a2+4) (a+2)

18、(a 2)(2) x2 2xy+ y2 9= (x y)2 32= (x y+3 ) (xy 3)(3) n2( m 2 ) + ( 2 m) = (m 2) (n21)= (m2)(n+1) (n1)27. (1) 2a3 8a=2a (a2 4) = 2a (a+2 ) (a 2)；4a (x y)2b (yx) =2 (xy) (2a+b)；(3) (x2+4 ) 216x2= ( X2+4+4 x)(x2+4 4x) =( x+2 ) 2 (x 2) 2;(4) 2xy x2+1y2= 1(x y) 2=(1+x y) (1x+y).28. ( 1) x3 4x = x(x2 4)=

19、x (x+2 )(x 2)(2) 2a2+4 a 2= 2 (a2 2a+1 ) = 2 (a1) 2(3) x2 5x 6 = (x-6) ( x+1 )(4) x24y2+x+2y=(x+2y) (x2y)+(x+2 y) = (x+2y) (x2y+1)29. ( 1 ) 4x2 36 =4 (x2 9) = 4 (x+3 ) (x 3)(2) 4m3+8 m2+32 m= 4m (m2 2m8)= 4m (m+2)(m4)(3) (y2 1) 26 (y21) +9 = (y213)2= (y+2) (y2)2= (y+2 )2(y2)2(4) a2+ac bc b2= (a+b) (

20、a b) +c(a b) = (a b) (a+ b+ c)30 . ( 1) 3x 12x3 = 3x (1 4x2) = 3x (1+2 x) ( 1 2x)(5) a3 4ab2= a(a24b2) = a (a+2b)(a2b)；(6) (2x+y) 2(x+2y) 2= (2x+yx2y)(2x+y+x+2y)= (xy)(3x+3y)=3(xy)(x+y)；(7) a2 4a+4c2= (a 2) 2 c2= (a 2+c) (a 2 c).31 . (1) 3ax 3ay2= 3a (x y2)；(a+b) 2 a2= (a+b a) (a+b + a) = b (2a+b)；(

21、8) 3a(X V)+9 (y x) = 3(x y)(a 3);(9) x4 18x2+81 = (x2 9) 2= (x+3 )2 (x3)2;(10) x2 5x+6 = (x 3) (x 2);(11) a2+2 a+1 b2= ( a+1 ) 2b2= ( a+1+ b)(a+1b).32 . (1) 3a512a4+9 a3=3a3 (a2 4a+3 )= 3a3(a3)(a 1) 3a26ab+3b212c2=3(a22ab+b24c2)= 3 (a b) 24c2 = 3 (a b+2c)(a b 2c)五.因式分解-十字相乘法等33. ( 1 )x2 5x 6=(x 6) (

22、x+1 )(2) 8x2 8x+2 =2 (4x2 4x+1 ) = 2 (2x 1 ) 2(3) a2 (xy) +b2(y x) = ( x y) (a2b2) = (xy) (a+b) (a b)34. ( 1 ) 9x2 25 = ( 3x+5 ) ( 3x 5) x4y4 8x2y2+16 = (x2y2 4) 2= (xy+2 ) 2 (xy 2) 2(3) a2(xy)b2(x y) =(a2b2)(x y) = (a+b) (a b) (x y)(4) x2 xy 6y2= (x 3y) (x+2 y)35. . (1) ax2 6ax+9 a= a (x2 6x+9 ) =

23、a (x 3) 2；(2) ( m+1 )( m 9)+8 m = m2 8m 9+8 m =m29= ( m+3 )(m3)；(3) a4+3 a24= ( a21) ( a2+4 ) = ( a 1) ( a+1) ( a2+4 ).36. (1) 6xz 9xy = 3x (2z 3y)(2) 8a3 8a2+2 a= 2a (4a2 4a+1 ) = 2a (2a 1) 2(3) 2ax218a3= 2a (x2 9a2) = 2a (x+3a) (x 3a)(4) x2 4x 12 = (x 6) (x+2 )37. (1) 3a2 6a+3=3 (a2 2a+1 ) =3 (a 1) 2;(2) a2 ab6b2= (a3b) (a+2b)；(3) 9a2 (2xy) + (y2x)= 9a2(2xy)( 2xy) = ( 2x y) (9a21)=(2x y) ( 3a+1 ) ( 3a 1).38. ( 1 ) x4 81 = (x2+9 )(x29) =