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# 整式除法和因式分解

1.计算：a7?a3? (?y)?(?y)? x8?x8? (mn)?(mn)?

x?x?x? (x?y)?(y?x)?

2．计算： 28ab?7ab? 24ab?(?6ab)? ?5xyz?15xy? 423253410753132876

(?5m2)2?5m4? 10xy3?(?5xy)? 7x(4x2y)2?7x3y2?

12423106 ?21ab?(?3ab)? (6?10)?(3?10)? ?8x2y3?6xy2? (?12x4y6)?x2y3)2?2

3．计算：(6a?8a)?(?2a)? (12x?6x?3x)?3x? (?8xy?5xy)?4xy? 43232322

(2a14b3?35a3b2?27a2b2?)?(7a2b ? ) [(a?b)?b(2a?b)?8a]?2a?

1143(0.25x2y?x3y2?xy)?(?0.5xy)2 26

z 8ab?2ab? 12abc?9ab? 4．因式分解：10x?5x? x?x? 8xy?12xy?

22(x?y)? 2x(y?z)?3(y?z) 6x(x?y)?4y(x?y)? 15x3?10x2? m(x2?y2)?n?232323222

3524 ) 2x(y?z)?5y(z?y)? 75xy?35xy? p(x?3)?2(?3x?

3 ?10m4n2?8m4n?2mn?132ab?2a2b? 5a(a?2b)2?20b(2b?a)2? 4

223225．因式分解：a?1? 4a?9? 25a?16b? xy?xy? 9x?4y? ?x?16? 224

1?36x2? 12a2?36b2? 0.81a2?36? x2?12y? x4?y4? 25

(a?x)2?(a?y)2? (a?b)(x?y)?(b?a)(x?y)? a3?9a?

6．因式分解；x?4xy?4y? x?2xy?y? 16a?2a4??9 x?4x?4? x?14x?49? 2222222

a2?12a?36? 4a2?4a?1? 25x2?8x0?0??1 x2?4xy?4y2? 6?4 25y2?1y

26xy2?9x2y?y3? ?a2?4ab?4b2? x2?2x(y?z)?(y?z)2? 4?12a(?b)?9a(?b) ?

(x?y)2?4x(x?y)?4x2?

?3xy2z2

231．是 次单项式，系数是 2．xy?3xy?2xy?2是次项式，常数项是7

3．请写出?abc的同类项 4.计算 (3a?ab?7)?(?4a?2ab?7)?

5.(?2xy) (?2a)?(?a) = 6.

8.(1.5?10)(7?10)? 6324222332

9.(a?b)? a2?b2? 10. (2x+3)(2x-3)= (-3a-2)(3a-2)=

11.(2m?1)= (?2ab)?(?3ab)? (

12. 多项式8ab?12abc中各项的公因式是13.4x?(322222322322y?7y2?y)?y? 533)2 x2?12x?36?()2 )?9?(

14. 16a2?9? a3b?ab?因式分解)

1.当x=2时,(x?x?5)?(2x?7x?3)?( ). A.8 B. -10 C. 20 D. -26

2.下面计算正确的有( )个 ①b?b?2b②x?x?x③(a)?a④x?x?2x⑤(a)?a?a ⑥(ab)?ab⑦(?2a)??4a⑧?(?a)?a A.0个 B. 1个 C. 2个 D. 3个

3.下列多项式的乘法中可用平方差公式计算的是( )

A.(x?)(x?1) B.(a?b)(b?23622333441652722432410222481

21a) C. (?c?b)(c?b) D. (x2?y)(x?y2) 2

2224.下列各式中,能够成立的等式是( ) 2A.(2x?y)?4x?2xy?y B.(x?y)?x?y C.(a?b)?2221

212a?ab?b2 D.(a?b)2?(b?a)2 4

5.在①x?x ②x?x?x ③(x) ④(x)?x中,结果为x的是( )A.①② B.①③ C.②③ D.③④

6.把?10ab?5b分解因式,正确的是( ) A. b(-10a+5) B.5b(-2a) C. -5b(2a+1) D. -5b(2a-1)

7.下列各式中不能用平方差公式分解因式,正确的是( )

A.?a?b B. ?x?y C. 49xy?z D.16m?25np

8.下面四个多项式完全平方式的是( )

A.m?mn?n B.x?2xy?y C.4a?2ab?2b D.222212210222352462222224222212x?xy?y2 4

9.为了便于直接运用于平方差公式,应将(x+y-z)(x-y+z)变形为( )

A.[(x+y)-z][(x-y)+z] B.[x+(y-z)][x-(y-z)] C.[(x-z)+y][(x+z)-y] D. [(x+y-z)][(x-y+z)]

1x与?2x2?xy?x的差 2. (3a+b)(3a-b)-b(a-b) 3. (2x?3)2?(x?1)(x?2) 2

112111224. (x?)(x?)(x?) 5. (2x?y?3) 6.化简求值:(2x?3y)?(2x?y)(2x?y),其中x?,y? 339321.?3x?2xy?2

1.6a(a?b)?4b(b?a) 2.?3ax?6axy?3ay 3.(a?2b)?(2a?b) 4.?1?81x

22224

5.(x?9)(x?1)?25 6.(x?y)?4x(x?y)?4x

1．梯形上、下底分别是4.25?10cm、8.95?10cm,高是1.6?10cm，求这个梯形的面积。

2．如图，某小区规划在边长为X m的正方形场地上，修建两条宽3m的道路，其余部分种草，表示出草坪的面积和道

33222米