整式的乘法训练专题解答.docx
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整式的乘法训练专题解答.docx
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整式的乘法训练专题解答
单项式的乘法法则:
单项式相乘,把它们的系数、相同字母分别相乘,对于只在一个单项式中含有的字母,则
连同它的指数作为积的一个因式
、计算与化简
1、(-5a2)(-3a)
=(-5)(-3)(a2*a)
=15a3
32
2、(2x)(-5xy)
^332、
=2x(-5xy)
2、
=8x(-5xy)
=8(-5)(x3x2)y
=-40x5y
232/32\2
3、xy(xy)
32
23232222
爲x3y2^--)2x2(y2)2
32
二一xy
3
(x3x2)(y2y4)
4、3x5*5x3
=(35)(x5x3)
5、4y・(-2xy3)
=4(-2)x(yy3)
c4
=-8xy
2
6、(-2.5x)*(-4x)
2
=(一2.5)(-4)(xx)
=10x37、
2523
=(2i56)(xx)(yy)z
2、3‘_2.
8(3xy)*(-4xy)
=33(x2)3y3・(Yxy2)
=27x6y3*(—4xy2)
632
=27(-4)(xx)(yy)
75
=-108xy
23、4/2.3
9、(-xyz)(-xy)
・(-x2)
4/2、4/3、4
=(-x)(y)(z)
4812/6、3
=xyz(「x)y
468312
=-(xx)(yy)z
101112
=一xyz
10、(-5an1b)(-2a)
=(一5)(—2)(an1a)b
=10an2b
2223
11、(-3ab)(-ac)*6ab(c)
=(-3ab)(-a2)2c2*6abc6
=(-3ab)a4c2*6abc6
=(-3)6(aa4a)(bb)(c2c6)
6^28
=-18abc
12、(-6an)*3anb
=(-6)3an2nb
n2
=-18ab
13、
8xnyn1
.3x2
3nn卅
=(82)(xx)(yy)
=12xn1y
n1n-21n2、
14、(—3xy)(xy)
6
1n1nn22、
=(-3)(-6)(xx)(yy)
1n1nn22
二—xy
2
12n1n4
=一xy
2
2
15、6abn•(-5anb)
=6(-5)(aan1)(bnb2)
=-30an11b
n乙n・2
=—30ab
16、(_3x)2<2xy2)2
=(-3)x2x(y)
4
=9x4xy
4
=94(xx)y
=36x4y4
17、6x2*3xy
2
=63(xx)y
=18x3y
2
18、(2ab)(-3ab)
=2(-3)(aa)(b2b)
=-6a2b
22
佃、(mn)(-mn)
(-m2n)
222
=-(mm)(nn)
2
20、(3xy)(-3xy)
=3(-3)(x2x)(yy)
^32
=-9xy
21、(4x4y)(-xy3)5
=(4x4y)(-x)5(y3)5
=(4x4y)(_x5)y15
=4(-1)(x4x5)y15
2342
22、(2xy)(-xy)
=23x3
/2、3/4、22
(y)(-x)y
=8x3y6
x8y
3862
=8(xx)(yy)
c118
=8xy
232
23、(-5ab)(2ab)
=(-5)2(a2a2)(b3b)
44
=-10ab
/325、
24、(ax)(bx)
3
325
=()()ab(xx5)
3
=^abx
12222
25、(xy)(2xy)
2
122222222=()(x)y2x(y)
2
14224
=xy4xy
4
=14(x4x2)(y2y4)
12222
26、(xy)(2xy)
2
122222222
=(飞)(x)y2x(y)2
14224
=xy4xy
4
=—4(x4x2)(y2y4)
4
66
=xy
12322
27、(—§axy)(3axy)
1、33,2、33
=(-?
a(x)y3ax(y)
=(-丄)a3x6y39a2x2y4
7
=(—)9(a3a2)(x6x2)(y3y4)27
1577
=axy
3
28、(ax2)(abxn)
=(aa)(x2xn)b
=a2bxn2
29、(2anb3)^^abn4c)
6
=2(-1)(ana)(b3bn4)c6
1n13nJ
=abc
3
1n1n2
=abc
3
n1n1nF、
30、(3xy)(xy)
3
=3(-寸)(xn1x)(ynyn1)
n11n"n1
二一xy
_xn2y2n1
312
31、(2c)(—abc)(-2ac)
4
132
=2(-2)(aa)b(ccc)
2
=-2a2bc6
32、—0.2xy2xy」y
5
=一by2」x2y
55
=0
7242.492.
33、
xyzxyz・(xyz)
4716
=一7-(一49)(x2xx)(yy2y)(zzz2)
4716
49444
=一一xyz
16
34、(-丄ab2c)2•(-1abc2)3・12a3b
23
1、22421x33363
=()abc()abc12ab
23
12,42,1x3363,
=abc()abc12ab
427
=1(—丄)(a2a3a3)(b4b3b)(c2c6)
427
1888
=abc
108
221332
-2(「abc)a(bc)-(-abc)・(一abc)
2
2、32、2,3246
36、(2xy)(3xy)4xy18xy
21
37、(2xy)(§xy)
12=2(xx)(yy)
3
二—xy
38、(_2a2b)(-3a)
=23a2ab3
^33
=6ab
54
39、(410)(510)
=451054
9
=2010
=21010
32
40、(5x)(2xy)
32
=52(xx)y
3
=10xy
41、(-3ab)(-4b2)
=(-3)(-4)a(bb2)
=12ab3
42、(2xy)3(—4xy2)
=2(x)y(-4xy)
=8x6y3(-4xy2)
=8(「4)(x6x)(y3y2)
=-32x7y5
3
43、(4xy)(—2xy)
二_8x2y4
2235
44、(匸xy)(xyz)
58
=—5(x2x)(y3y)z
58
134
=xyz
4
23223
45、(-xyz)(-xy)
246/6、3
=xyz(-x)y
876
=一xyz
38
46、(210)(810)
=281038
11
=1610
12
=1.610
单项式乘以多项式
单项式乘以多项式就是用单项式去乘以多项式的每一项,再把所得的积相加
m(abc)二ambmcm
二、计算与化简:
1、(-4x)*(2x23x-1)
=一4x2x-4x3x4x
=-8x3-12x4x
221
2、(ab-2ab)ab
32
2211
=abab-2abab
322
12」32」2
=一ab-ab
3
3、(x_3y)(_6x)=-x6x3y6y
2
=—6x18xy
4、5x(2x-3x4)
2
=5x2x—5x3x5x4
=10x3-15x20x
222
5、x(x3)x(x-3)-3x(x-x-1)
2222
=xxx3xx-x3-3xx3xx3x
3323
=x3xx「3x「3x3x3x
=-x33x26x
丄32
=3xy(3xyxy)
2
32
=3xy3xy3xyxy
2
932
==9xyxy
2
=3x2y3xy-x2y3xy
3232
=9xy-3xy
2
8(4ab-b)・(-2bc)
2
=-■4ab2bcb2bc
=-8ab2c2b3c
21
9、2x(xx1)
2
21
=2xx-2x-x2x
2
=2x3-x22x
10、5ab(2a-b0.2)
=5ab2a-5abb5ab0.2
=10a2b-5ab2ab
224
11、(-3x2)(4x2x1)
9
22242
=一3x4x3x—x—3x
9
=-12x44x3-3x2
3
4
12、(2aa)*(-9a)
39
224
=-2a9aa9a9a
39
=-18a36a24a
2223
13、(-2ab)*(3ab-2ab-4b)
=(-2)2a2(b2)2・(3a2b-2ab-4b3)
=4a2b4・(3a2b-2ab-4b3)
„2.4-2.„2,4^,„243
=4ab3ab-4ab2ab-4ab4b
4,5n3527
=12ab「8ab「16ab
321253\/‘2\
14、(匚xyxyy)<-4xy)
426
322122532
=xy4xyxy4xyy4xy)
426
小33^242105
=一3xy2xyyxy
3
15、3x2♦(「3xy)2「x2(x2y2「2x)
22222222
=3x(-3)xy-xxyx2x
小2小2242小3
=3x9xy-xy2x
=9xy-xy2x
c42c3
=8xy2x
16、5x(x2-2x4)x2(x-1)
222
=5xx-5x2x5x4xx-x1
=5x3TOx220xx3「x2
22
=(51)x(-10-1)x20x
=6x3-11x220x
3ab(a2b-ab2ab)「ab2(2a2「3ab2a)
222222
=3abab-3abab3abab-ab2aab3ab-ab2a
=3a3b2-3a2b33a2b2-2a3b23a2b3-2a2b2
=(3-2)a3b2(-33)a2b3(3-2)a2b2
111
18、(m1)(2m-1)(m-5)
236
112115
=一m___m__m
223366
(1-21)m(1
2362
19、t3—2tt-2(t-3)I
32
=t-2t(t-2t6)
=t3-2t34t2-12t
32
=(1_2)t34t2-12t
32
=-14t12t
20、2ab(5ab23a2b)
=2ab5ab22ab3a2b
2,3^32
=10ab6ab
221
21、(一ab-2ab)ab
32
2211
=一abab-2ab—ab
322
12322
=ab-ab
3
2
22、5x(2x-3x4)
2
=5x2x-5x3x5x4
=10x3-15x220x
21,2
23、-2a(—abb)
2
c322
=一2ab-2ab
212
24、(一xy-6xy)xy
-2
212
-6xyxy
2
3一
221=xyxy
32
1
=x
3
3y3-3x2y3
25、
122
(xy-2xyy)3xy
2
122
=xy3xy-2xy3xyy3xy2
332小22小3
=—xy-6xy3xy
2
232
26、2a(a3a-2)-3(a2a-a1)
=2aa22a3a-2a2-3a332a23a-31
=2a36a2-3a36a23a-3
32
=-a12a3a-3
三、解方程
2(5x-4)-3(x6)=5(x-1)-x
解:
10x-8-3x-18=5x-5-x
10x-3x-5xx--5818
3x二21
x=7
多项式的乘法
多项式乘以多项式就是用其中一个多项式的每一项去乘以另一个多项式的每一项,再把所
得的积相加;
(ab)(m■n)二amanbmbn
四、计算
1、(x2y)(5a3b)
=x5ax3b2y5a2y3b
=5ax3bx10ay6by
2、(2x-3)(x4)
=2xx2x4-3x-34
2
=2x8x-3x-12
2
=2x5x-12
3、(3xy)(x-2y)
22
=3x-3x2yxy_2y
=3x2-6xyxy_2y2
=3x2_5xy_2y2
4、(xy)(x-y)
-xyxy「y2
22
=x「y
5、(xy)2
=x2xyxyy2
2小2
=x2xyy
6、(mn)(mn)
=m2mnmnn2
2小2
=m2mnn
7、(xy)(a-b)
=xa-xbya-yb
=ax-bxay-by
2
8(ab)
=a2ababb2
=a22abb2
9、(a-b)2
22
=a-ab-abb
=a2-2abb2
10、(8y5)(8y-5)
=8y8y-8y558y_55
=64y2_40y40y_25
2
=64y-25
11、(m2n)(m-2n)
2
=m-m2n2nm-2n2n
=m2-2mn2mn-4n2
2.2
=m-4n
12、(2n6)(n-3)
=2nn-2n36n-63
2
=2n-'6n,6n—18
13、(2x3)(3x-1)
=2x3x-2x133x-31
2
=6x-2x9x-3
2
=6x7x-3
14、(2a3b)(2a-3b)
=2a2a-2a3b3b2a-3b3b
22
=4a-6ab6ab-9b
22
=4a2-9b2
15、(2a-3b)(a5b)
=2aa2a5b-3ba-3b5b
=2a210ab-3ab-15b2
=2a27ab-15b2
16、(3x2y)(3x-2y)
=3x3x-3x2y2y3x-2y2y
=9x2-6xy6xy_4y2
=9x2-4y2
17、(xy)2
=x2xyyxy2
2^2
=x2xyy
18、(2ab)2=2a2a2abb2ab
22
=4a2ab2abb
22
=4a4abb
2
19、(2x5)
=2x2x2x552x55
2
=4x10x10x25
2
=4x20x25
20、(x30)(x40)
2
=x40x30x3040
2
=x70x1200
21、(x30)(x-40)
=x-40x30x-3040
2
=x-10X-1200
22、(1-x)(0.6-x)
2
=10.6-x-x0.6x
24、(m2n)(m-2n)
2
=m「m2n2nm「2n2n
22
=m-2mn2mn-4n
2.2
=m-4n
25、(2n5)(n-3)
=2nn-2n35n「53
2
=2n-6n5n-15
2
=2n「n「15
26、(x2y)
2
=x2x2y2yx2y2y
22
=x2xy2xy4y
22
=x4xy4y
27、(axb)(cxd)
=axcxaxdbcxbd
2
=acxadxbcxbd
28、(2x3)(-x-1)
=-2xx-2x1-3x-31
2
=-2x-2x-3x-3
=ax2bxay2by
3
30、(2a3)(b5)
2
33
=2ab':
,2a:
:
5■3b■:
22
9
=3ab10ab152
31、(-2m-1)(3m-2)
=-2m3m2m2-13m12
2
=-6m4m-3m2
2
=「6mm2
2
32、(x-y)
2.2
=x_xy_yxy
22
=x-2xyy
2
33、(-2x3)
=2x2x-2x3-32x33
2
=4x-6x-6x9
=4x-12x9
34、(abc)(cde)
、、、、、、2
=acadaebcbdbeccdce
2x
2
5x-x二
6-
4
5x
-2
2
x:
=—
5
2、
3x(x2)-
2(x
5)
=(x_2)(x3)
3x
26x—2x2
-10
2=x
3x-2x-6
3x
26x-2x2
-x2
-3x
2x=-610
5x
=4
4
x:
——
5
3、(x3)(x_4)=x2-16
x2-4x3x-12二x2-16x2-4x3x-x2=-1612
_x=-4
x=4
4、3x(x2)(x_1)(x1)=4(x28)3x26xx2-1=4x232
3x26xx2-4x2=321
6x=33
3311
x=
62
2
5、2x(x-3)-(x-3)(x6)=x12
-9x--6
2
x=
3
2
6、2(x-2)-6x(x-1)=4x(1-x)
222
2x-4-6x6x=4x-4x
222
2x-6x4x6x-4x=4
2x=4
x=2
2
7、x(x3)—x(1—2x)=93x
x23x「x2x2二93x2
222
x3x-x2x-3x=9
2x=9
9
x=—
2
8、(2x3)(x-1)-28二(1x)(2x11)
22
2x-2x3x-3-28=2x112x11x
2x2-2x3x—2x—2x2—11x=〔11328
-12x=42
7
x=__
2
9、(x-3)(x-2)18=(x9)(x1)
22
x-2x-3x618=x10x9
x「2x-3x-x-10x二9「6「18
-15x二-15
x=1
六、计算与化简
2
=x3x2x6
2
=x5x6
2、(x-4)(xT)
=x2x-4x-4
=x2-3x-4
3、(y4)(y-5)
2
=y_5y4y_20
2
=y-y-20
4、(y-3)(y-5)
2
=y_5y_3y15
5、(x-6)(x7)
2
=x7x-6x「42
=x2
x—42
-2…
.11
-yy
32
ii
y--
66
6、(x6)(x-8)
2
=x—8x6x—48
=x2-2x-48
1丄1
7、(y)(y)
23
6
11
8、(y沙5)
111—y—y亠—
5420
91
y
2020
9、(7x8)(6x-5)
2
=42x-35x48x-40
2
=42x—13x—40
10、(3x-2)(4x5)
2
=12x15x-8x-10
=12x13x-10
11、(2a3)(a-5)
2
29
=3aTOaa「15
2
=3x2
=3x2
=3x2
3
x
8
3
x
8
189
24x—3
192-3
8
x-3
8
13、(x3)(x4)-x(x1)-14
22
=x4x3x12-(xx)-14
14、(3y-1)(2y-3)(6y-5)(y-4)
22
=6y-9y-2y3(6y-24y_5y20)
22
=6y_9y_2y36y_24y_5y20
=-40y23
七、解方程
2
1、(x3)(x「4)=
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