一、判断题。
1. ( )
2.=x2-y2 ( )
3. ( )
4. ( )
5. 3a3x-4b3y+3b3x-4a3y=(a3+b3)(3x-4y) ( )
6. (x-y)4+x(y-x)2+y(y-x)3=2(x-y)2(x-y+1) ( )
7. 整式和分式统称有理式. ( )
8. x2-16y2-8y-1=(x+4y+1)(x-4y+1) ( )
9. ( )
10. 把一个多项式化成几个整式的积的形式叫做多项式的因式分解. ( )
11. ( )
12. a2+2ab+b2=(a+b)2 ( )
13. -4x3+8x2-4x=-4x(x-1)2 ( )
14. ( )
15. ( )
16.甲用x小时走完s千米, 乙比甲早出发a小时, 早到b小时,那么乙每小时走千米. ( )
17. ( )
18. 25y2-4a2-12ab-9b2=(5y+2a+3b)(5y-2a+3b) ( )
19. 用A、B表示两个整式, 如果B中含有字母, 式子就叫做分式. ( )
20. ( )
21. 2a6-32a2b4 =2a2(a2+4b2)(a+2b)(a-2b) ( )
22. ( )
23. ( )
24. -x3y3-x2y2+xy=-xy(x2y2+xy-1) ( )
25. -8a3+27b3 =-(2a-3b)(4a2+6ab+9b2) ( )
26. 361-(3a+2b)2=(19-3a-2b)(19+3a+2b) ( )
27. ( )
28. a2+b2-9c2-1-2ab-6c=(a-b-3c-1)(a-b+3c+1) ( )
29. (x+2)(x-3)(x2-7)+(2+x)(3-x)(x+3)=(x+2)(x-3)(x2+x-4) ( )
30. 10ab-3+6b-5a=(5a+3)(2b-1) ( )
31. 873-763是11的倍数 ( )
32. (m-n)2-2(m2-n2)+(m+n)2=2n2 ( )
33. 2-2a4=2(1+a2)(1+a)(1-a) ( )
34. ( )
35. m2-n2-m+n=(m-n)(m+n-1) ( )
36. ( )
37. x3-2x2y+xy2=x(x-y)2 ( )
38. 当x=-3时, ( )
39. ( )
40. x2-2xy+y2-1=(x-y+1)(x-y-1) ( )
41. 将a2-b2+2b-1分解因式得(a+b-1)(a-b+1) ( )
42. 12x5-24x3+18x2=6x2(2x3-4x+3) ( )
43. ( )
44. ( )
45. ( )
46. 25x2y4z16-1=(5xy2z4-1)(5xy2z4+1) ( )
47. x2(x+1)-y(xy+x)=x(x-y)(x+y+1) ( )
48. -am-1+14am-49am+1 =-am-1(1-7a)2 ( )
49. ab(x2+1)+x(a2+b2)=(a+bx)(b+ax) ( )
50. a4-3a3+3a2-a=a(a-1)3 ( )
51. 1-x6=(1-x3)(1+x3)=(1-x)(1+x)(1-x+x2)(1+x+x2) ( )
52. a9-ab2=a(a4+b)(a4-b) ( )
53. x3m+3-y3=(xm+1-4y)(x2m+2+4xm+1y+16y2) ( )
54. am-1-am+2+am-am+1=am-1(1+a)2(1-a) ( )
55. a2(a+1)-b2(b+1)=(a-b)(a2+ab+b2+a+b) ( )
56. ( )
57. (x+1)2+x(3x+2)=(2x+1)2 ( )
58. 5x2m+3y4n+2-10x3m+7y2n+1=5x2m+3y2n+1·(y2n+1+2xm+4) ( )
59. a2n+an+1-an=an(an+a-1) ( )
60. ( )
61. 8m3(m2-n2)-27n6(n2-m2)=(m2-n2)(2m+3n2)(4m2-6mn2+9n4) ( )
62. 8a3(x3-y6)+(y6-x3)=(x-y2)(x2+xy2+y4)(2a-1)(4a2+2a+1) ( )
63. a8-81b8=(a4-9b4)(a4+9b4) ( )
. a16-b16=(a-b)(a+b)(a2+b2)(a4+b4)(a8+b8) ( )
65. a4-4a3+4a2-9=(a2-2a-3)(a2-2a+3) ( )
66. ( )
67. a2-b2+m2-n2+2(am-bn)=(a+m+b +n )(a+m-b -n ) ( )
68. ab(c2-d2)-cd(a2-b2)=(ac+bd)(bc-ad) ( )
69. 1+12x2y2+48x4y4+x6y6=(1+4x2y2)3 ( )
70. x5+x4y+2x3y2+2x2y3+xy4+y5=(x+y)(x2+y2)2 ( )
71. -am+1y2n-1+am-1y2n+1=am-1y2n-1(-a2+y2) ( )
72. 2(a2-3mn)+a(4m-3n)=(a+2m)(2a-3n) ( )
73. ( )
74. (a+b+c)3-(a3+b3+c3)=3(a+b)(b+c)(a+c) ( )
75. a3m-a3m+3=a3m(1-a)(1+a+a2) ( )
76. 343m6-125n12=(7m2-5n4)(49m4+35m2n4+25n8) ( )
77. 1+x+x(x+1)+x(x+1)2+x(x+1)3=(1+x)4 ( )
78. am+4-8am+3-16am+2=am+2(a2-8a-16) ( )
79. x3-x2-x-y3+y2+y=(x-y)(x2+xy+y2-x-y-1) ( )
80. (x+y)3+2xy(1-x-y)-1=(x+y-1)(x2+y2+x+y+1) ( )
81. -12a2m+1bm+2+20am+1b2m+4=-4am+1bm+2(3am-5bm+2) ( )
82. am+3-amb3=am(a-b)(a2+ab+b2) ( )
83. (a-b)n+3-(a-b)n=(a-b)n(a-b-1)(a2+b2-2ab+a-b+1) ( )
二、单选题。
84. 的结果是 [ ] A.a+5 B. C.a2-1 D.a2-a+1
85. 4xy+2y-8x-y2的结果是 [ ] A.(4y+x)(y-2) B.(4x-y)(y -2) C.(4x+y)(y+2) D.(4x+y)(y -2)
86. 当x=____时, 分式没有意义. [ ] A.x=3 B.x=-3 C.x=±3 D.x=4
87. 等于 [ ] A. B. C. D.
88. [ ] A.- B. C. D.-
.4a2-b2+c2-4ac等于[ ]
A.(2a-c+b)(2a+c-b) B.(2a-c+b)(2a-c-b) C.(2a+c+b)(2a-c-b) D.(2a+c-b)(2a-c-b)
90. 若代数式有意义, 则x的取值范围是 [ ]
A.x≠1, x≠- 2 B.x≠1, x≠2 C.x≠1, x≠-2, x≠2 D.x≠1, x≠-2, x≠2, x≠-1
91. a2-2ab+b2-c2等于[ ] A.(a-b+c)(a-b-c) B.(a+b+c)(a-b-c) C.(a-b+c)(a+b-c) D.(a-b+c)(a+b+c)
92. 已知 的值是 [ ] A.- B. C.- D.
93. 54-2y3等于 [ ] A.2(3-y)(9+3y+y2) B.(3-y)(9+3y+y2) C.(27-y3) D.2(27-y3)
94. a2(x-2a)2-a(2a-x)2 因式分解的结果是 [ ]
A.a(x-2a)2(a-1) B.(x-2a)2(a2-a) C.a(x-2a)2(a+1) D.(x-2a)2(a2+a)
95. 使分式有意义的条件是 [ ] A.x≠2 B.x≠-2 C.x≠2且x≠-2 D.x≠0
96. 已知 的值为 [ ] A.-1 B.1 C.1 D.
97. 计算的结果是 [ ] A. -1 B. 0 C. 1 D. 2
98. x3-xyz+x2y-x2z等于 [ ] A.(x-y)(x2-xz) B.(x+y)(x2-xz) C.x(x+y)(x+z) D.x(x+y)(x-z)
99. 计算: [ ] A. B. C. D.
100. 若分式无意义,则[ ] A. x=1 B. x=-1 C. x=1或x=-1 D.没有这样的有理数
101. -a2-14ab-49b2=[ ] A.(a+7b) B.-(a+7b)(a-7b) C.-(a+7b)2 D.(a+7b)2
102.=[ ] A. B. C. D.-
103. x2+6x+9等于[ ] A.(x-3)2 B.(x+3)2 C.(x-3)3 D.(x+3)3
104. 下列等式中,正确的是:[ ] A. B.=-1 C. D.
105. 下列等式中正确的是 [ ]
A. B. C. D.
106.=[ ] A.x-1 B.-x+1 C.-x-1 D.x+1
107. ÷ax的结果是 [ ] A. B. C. D.
108. 的结果是 [ ] A. -2 B. 2 C. -1 D. 1
109. 的结果是 [ ] A. B.- C. D.
110. 3x2-3y2等于 [ ] A.(x-y)(x+y) B.3(x-y)(x+y) C.3(x-y)2 D.3(x2-y2)
111. [ ] A. B.- C.- D.-
112. 5a2-7a-5ab+7b等于 [ ] A.(a-b)(5a-7) B.(a+b)(5a-7) C.(a+b)(5a+7) D.(a-b)(5a+7)
113. a2-b2+4b-4等于 [ ] A.(a+b-2)(a-b+2) B.(a-b-2)(a-b+2) C.(a+b+2)(a-b+2) D.(a+b-2)(a+b-2)
114. 的结果是 [ ] A. -a-5 B. -a+5 C. a-5 D. a+5
115. 下列各式中, 正确的是[ ] A. B. C. D.=a+b
116. a2b+a2-4b-4等于 [ ] A.(b+1)(a+2) B.(b+1)(a-2) C.(b+1)(a+2)(a-2) D.(b+1)(a2-4)
117. 如果分式的值为零, 那么x的值为 [ ] A.30 B.0 C.1 D.2
118. -7ab+21abx-28aby等于 [ ] A.-7(ab+3x+4y) B.-7ab(1-3x+4y) C.-7ab(4y-3x) D.7ab(1-3x+4y)
119. 若1<x<2, 则分式的值为 [ ] A. -1 B. 3 C. 1 D. 2
120.的结果是 [ ] A. B. C. D.
121. x3+x-y-y3等于[ ] A.(x+y)(x2-xy+y2+1) B.(x-y)(x2+xy+y2+1) C.(x2+xy+y2)(x-y) D.(x2-xy+y2+x)
122.=[ ] A. B. C. D.
123. [ ] A. B.- C.- D.
124. 的结果是 [ ] A. -1 B. 0 C. 1 D. 2
125. 等于 [ ] A. B. C. D.
126. 下列因式分解,完全正确的是 [ ]
A. B.
C. D.
127. 多项式2a2+2ab+b2分解因式的结果是[ ] A.2(a+b)2 B.(2a+b)2 C.(2a+b)2 D.
128. 分式的值为零时, x的值是 [ ] A.2 B.-1 C.2, -1 D.3, -1
129. 已知x为非零实数,那么的值是[ ] A.-1或3 B.1或3 C.-1或-3 D.1或-3
130. m2n-mn2-3m+3n等于 [ ] A.(m-n)(mn-3) B.(m+n)(mn-3) C.(m+n)(mn+3) D.(m-n)(mn+3)
131. 25x2-9y2等于 [ ] A.(5x+3y)(5x-y) B.(5x-3y)2 C.(5x+3y)(5x-3y) D.(25x+9y)(x-y)
132. =等于 [ ] A.- B. C. D.-
133. 计算= [ ] A. - B. - C. D.
134. 1-n4等于 [ ] A.(1+n2)(1-n)2 B.(1+n2)(1+n)(1-n) C.(1+n)2(n-1)(1-n) D.(1+n2)(n-1)(1+n)
135. 当-3 137. 已知的值为 [ ] A. B. C.- D.- 138. 在分式中, 当a=________时分式无意义. [ ] A.0 B.2 C.-2 D.1 139. a3+a2-2ab+b2-b3等于 [ ] A.(a+b)(a2+ab+b2+a-b) B.(a-b)(a2-ab+b2+a-b) C.(a-b)(a2+ab+b2+a-b) D.(a-b)(a2-ab-b2-a+b) 140. 在有理数范围内,4x-x5等于 [ ] A.x(2+x2)(2-x2) B.x(2-x)2 C.x(2+x2)2 D.x(2+x2) 141. 8x2y2-16xy+8等于 [ ] A.(xy-1)2 B.(xy+1)2 C.8(xy-1)2 D.8(xy+1)2 142. x2y-x2z+y2z-y3等于 [ ] A.(y-z)(x2-y2) B.(y-z)(x-y)(x+y) C.(y-z)2(x-y) D.(y-z)(x+y)2 143. 2x3+16等于 [ ] A.(x+2)(x2-2x+4) B.2(x+2)(x2+2x+4) C.2(x+2)(x2-2x+4) D.2(x+2)(x2-2x-4) 144. x2-y2+3x+3y等于 [ ] A.(x+y)(x+y-3) B.(x-y)(x+y+3) C.(x+y)(x-y-3) D.(x+y)(x-y+3) 145. 的结果是 [ ] A. - B. - C. D. 146. x2-4y2+x+2y等于[ ] A.(x+2y)(x-2y+1) B.(x-2y)(x-2y+1) C.(x+2y)(x+2y+1) D.(x+2y)(x-2y-1) 147. 等于 [ ] A. B. C. D. 148. x2+y2-z2+2xy等于[ ] A.(x+y+z)(x+y-z) B.(x-y-z)(x+y+z) C.(x-y-z)(x+y-z) D.(x-y+z)(x+y-z) 149. 等于 [ ] A. B. - C. - D. - 150. (a+2b)2-(x-3y)2等于 [ ] A.(a-2b-x+3y)(a-2b-x-3y) B.(a+2b-x-3y)(a+2b-x-3y) C.(a+2b+x-3y)(a+2b-x+3y) D.(a-2b+x-3y)(a-2b-x+3y) 151. a3-b3的结果是: [ ] A.a3-b3=(a-b)(a2+2ab+b2) B.a3-b3=(a-b)(a2-2ab+b2) C.a3-b3=(a-b)(a2-ab+b2) D.a3-b3=(a-b)(a2+ab+b2) 152. 8x6+x3等于 [ ] A.x3(2x+1)(4x2-2x+1) B.x3(2x-1)(4x2-2x+1) C.x3(2x+1)(4x2+2x+1) D.x3(2x+1)(4x2+2x-1) 153.下列分式中, 与分式的值相等的是[] A. B.- C. D.- 154. 已知x=3y, 则的值为 [ ] A. B. C.- D.- 155. a3-ab2+a-b等于[ ] A.(a-b)(a2+ab+1) B.(a-b)(a2-ab+1) C.(a+b)(a2+ab+1) D.(a+b)(a2+ab-1) 156. a2-20a+100等于 [ ] A.(a+10)2 B.(a-1)2 C.(a-10) D.(a-10)2 157. 若分式的值等于零, 则x的值为 [ ] A.1 B.±1 C. D.-1 158. [ ] A. B. C. D. 159.把分式中的x和y都扩大3倍,那么分式的值 [ ] A.扩大了3倍 B.不变 C.缩小了3倍 D.扩大了9倍 160. 分式恒等于[ ] A. B. C. D. 161. x2-y2+2x+1等于[ ] A.(x+y+1)(x-y+1) B.(x-y+1)(x-y-1) C.(x+y-1)(x-y-1) D.(x+y-1)(x-y+1) 162.的结果是 [ ] A. B. C. D. 163. 的结果是 [ ] A. x-4 B. x-5 C. x-6 D. x-7 1. 下列各恒等变形中, 是因式分解的是: [ ] A.a2-2ab+b2=(a-b)2 B.(a+b)2=a2+2ab+b2 C.a2b+ab2+c=ab(a+b)+c D.a2-2ab+b2-c=(a-b)2-c 165. 4xy+1-4x2-y2等于 [ ] A.(1+2x-y)(1-2x+y) B.(1+2x+y)(1+2x-y) C.(1-2x-y)(1+2x+y) D.(4-2x+y)(2-3x-y) 166. 的值= [ ] A. B. C. D. 167. -xy等于 [ ] A. B. C. D. 168. 计算的结果是 [ ] A. B. C. D. 169. 16x2+56xy+49y2等于 [ ] A.(4x-7y)2 B.(4x+7y)2 C.(4x+y)2 D.(x+7y)2 170. 4-4a2+8ab-4b2分解因式的结果是 [ ] A.4(1-a+b)(1+a-b) B.(2-2a+2b)(2+2a+2b) C.(2-2a+2b)(2+2a-2b) D.4〔1-(a-b)2〕 171. (x-3)(3x-2)-7(x-3)的结果是[ ] A. 3(x-3)(x-3) B. (x-3)(3x-9) C. 3(x-3)2 D. 3(x-3) 172. [ ] A. B. C. D. 173. 等于 [ ] A. B. C. D. 174. 当x=_____时, 分式没有意义. [ ] A.-4 B.0 C.4 D.1 175. 多项式a2-36b2分解因式的结果是:[ ] A.(a2-6b)(a2+6b) B.(a+6b2)(a-6b2) C.(a+6b)(a-6b) D.(a+36b)(a-36b) 176. 下列因式分解正确的是 [ ] A.B.C.D. 177. x3-xy2 因式分解的结果是 [ ] A.x(x2-y2) B.x(x-y)2 C.-x(x2+y2) D.x(x-y)(x+y) 178. 分解因式a2b2-b4等于: [ ] A.b2(a+b)(b-a) B.b2(a-b)2 C.b2(a+b)(a-b) D.b2(a+b)2 179. xn-ym分解因式为(x-y)(x2+xy+y2),那么m、n的值是 [ ] A.m=3,n=3 B.m=2,n=2 C.m=3,n=2 D.m=4,n=4 180. 使分式的值为正的条件是 [ ] A.x< B.x> C.x<0 D.x>0 181.多项式m(a-2)+(2-a)分解因式的结果是[ ] A.(a-2)(m+1)B.(a-2)(m-1)C.(2-a)(m+1)D.(2-a)(m-1) 182. [ ] A. -a3 B. -a4 C. -a5 D. -a6 183. 18x3nym+27xny2m的公因式是 [ ] A.3xnym B.9xnym C.3xnym+1 D.9xny2m 184. x2y2+x2y-4xy-2x+4等于 [ ] A.(xy-2)(y+x+2) B.(xy+2)(xy+x-2) C.(xy-2)(xy+x-2) D.(xy-2)(xy-x+2) 185. 在有理数范围内 a8-81b8等于 [ ] A.(a2-3b2)2(a2+3b2)2 B.(a4-9b4)(a4+9b4) C.(a4+9b4)(a2-3b2)(a2+3b2) D.(a4-9b4)2 186. = [ ] A.a B.-a C.a2 D.2a 187. 等于 [ ] A. 1 B. 2 C. 3 D. 4 188. 将多项式16x8-1在有理数范围内分解因式, 正确的结果是: [ ] A.(4x4+1)(4x4-1) B.(4x4+1)(2x2+1)(2x2-1) C.(2x2+1)2(2x2-1)2 D.(2x2+2x+1)(2x2-2x+1)(2x2+1)(2x2-1) 1. 多项式 am-1-am+2+am+am+1的公因式是: [ ] A.am B.am-1 C.am+1 D.am+2 190. 2x3n-12x2ny2+18xny4等于 [ ] A.2xn(xn-3y2)2 B.2xn(xn-3y2) C.xn(2xn-6y2)2 D.2x(xn-3y2)2 191. 的结果是 [ ] A.- B.- C. D. 192. 的结果是 [ ] A. -2 B. -1 C. 1 D. 2 193. 把27x2n-3x2n+2(n为自然数)分解因式是: [ ] A.3x2n(9-x2) B.3x2n(3+x)(3-x) C.3xn(3+x)(3-x) D.以上答案都不对 194. a6+a4-a2-1 [ ] A.(a-1)3(a+1)3 B.(a+1)2(a-1)2 C.(a2+1)2(a+1)(a-1) D.(a2+1)2(a+1) 195. 将多项式: -5x2m+1yn+2-15xm+1y2n+1因式分解的正确结果是: [ ] A. -5xm+1yn+2(xm+3yn-1) B. -5xmyn(xm+1y2+3xyn+1) C. -5x2m+1y2n+1(y-n+1+3x-m) D. -5xy(x2myn+1+3xmy2n) 196. ambn-anbm(其中m>n)分解因式的结果是 [ ] A.ambn(1-bm-n) B.anbn(am-n-bm-n) C.ambm(bn-an) D.ab(am-1-bm-1) 197. 如果a+b=2c,且a≠b,则= [ ] A.-4 B.-2 C.0 D.2 198. 的结果是 [ ] A. B. C. D. 199.a5-a3+a2-1等于[ ]A.(a2-1)(a3+1)B.(a+1)2(a-1)(a2-a+1)C.(a+1)(a-1)(a3+1)D.(a-1)2(a+1)(a2-a+1) 200. 多项式-3x2n-9xn分解因式, 其结果是: [ ] A.3(-x2n+3xn) B.-(x2n-3xn) C.-3xn(xn+3) D.-3xn(x2+3) 三、填空题。 201. 已知: a+2b=100, a-2b=0.01, 则 5a2-20b2的值是_________. 202.的值等于零时, x的取值为______. 203. 当x=_______时,分式的值是零. 204. 已知 a-b-c=-5, 则 a(a-b-c)+b(c-a+b)+c(b+c-a)的值是____________. 205.=___________ 206. =_________ 207. 当 x=-1, a=296, b=-307, c=2009时, x(a+b-3c)-(3c-a-b)的值是____. 208. 已知: a-b=1, 则 a3-b3-3ab=________. 209. 已知: x+y=-2, a+b=, x2-xy+y2=-1, 求bx3+ay3+by 3+ax3的值是____________. 210. 当x=______时, 分式没有意义. 211.=___________ 212. 当m=__________时,分式的值为0. 213. 已知=2000,则的值为_______. 214. 在分式中当a=_______时分式的值为零. 215. 当x=3时,分式,则m=________. 216. 当x=_____时,分式的值为零. 217.=_________ 218.=_________ 219.=_____ (用分数表示) 220. 填写下式变形的依据: 依据________ , = 依据________ _. 答案部分 一、 1. F 2. F 3. F 4. T 5. F 6. F 7. T 8. F 9. T 10. T 11. T 12. T 13. T 14. F 15. T 16. T 17. F 18. F 19. T 20. T 21. T 22. T 23. T 24. T 25. T 26. T 27. T 28. T 29. F 30. T 31. T 32. F 33. T 34. T 35. T 36. T 37. T 38. T 39. T 40. T 41. T 42. T 43. F 44. F 45. T 46. F 47. T 48. T 49. T 50. T 51. T 52. T 53. T 54. T 55. T 56. T 57. T 58. F 59. T 60. F 61. F 62. T 63. F . T 65. F 66. T 67. T 68. T 69. T 70. T 71. F 72. T 73. T 74. T 75. T 76. T 77. T 78. T 79. T 80. T 81. T 82. T 83. T 二、 84. A 85. B 86. C 87. A 88. A . B 90. C 91. A 92. B 93. A 94. A 95. C 96. C 97. A 98. D 99. C 100. D 101. C 102. C 103. B 104. B 105. D 106. C 107. A 108. D 109. B 110. B 111. D 112. A 113. A 114. D 115. C 116. C 117. C 118. B 119. C 120. C 121. B 122. A 123. B 124. C 125. C 126. D 127. B 128. A 129. A 130. A 131. C 132. B 133. B 134. B 135. A 136. B 137. A 138. C 139. C 140. A 141. C 142. B 143. C 144. D 145. C 146. A 147. B 148. A 149. C 150. C 151. D 152. A 153. D 154. A 155. A 156. D 157. A 158. C 159. B 160. D 161. A 162. D 163. B 1. A 165. A 166. D 167. A 168. C 169. B 170. A 171. C 172. A 173. C 174. A 175. C 176. D 177. D 178. C 179. A 180. B 181. B 182. C 183. B 184. C 185. C 186. A 187. A 188. D 1. B 190. A 191. C 192. C 193. B 194. C 195. A 196. B 197. D 198. C 199. B 200. C 三、 201. 5 202. 3 203. -5 204. 25 205. -b 206. 1 207. 0 208. 1 209. -1 210. 4 211. a 212. -2 213. -1999 214. 2 215. -9 216. -1 217. 1/3 218. 3 219. 1/2 220. 提取公因式; 分式的基本性质。