整式的乘法同步測(cè)試班級(jí) 姓名 成績(jī) 一、選擇題：(60)1下列各式中，正確的是（ ）At5t5 = 2t5Bt4+t2 = t 6 Ct3t4 = t12 Dt2t3 = t5 2下列計(jì)算錯(cuò)誤的是（ ）Aa2(a)2 = a4 B(a)2(a)4 = a6C(a3)(a) 2 = a5 D(a)(a)2 = a33下列計(jì)算中，運(yùn)算正確的個(gè)數(shù)是（ ）5x3x3 = x3 3m2n = 6m+nam+an = am+n xm+1xm+2 = xmxm+3A1 B 2 C3 D44計(jì)算a6(a2)3的結(jié)果等于（ ）Aa11 Ba 12 Ca14 Da365下列各式計(jì)算中，正確的是（ ）A(a3)3 = a6 B(a5)4 = a 20 C(a)53 = a15 D(a)23 = a66下列各式計(jì)算中，錯(cuò)誤的是（ ）A(m6)6 = m36 B(a4)m = (a 2m) 2 Cx2n = (xn)2 Dx2n = (x2)n7下列計(jì)算正確的是（ ）A(xy)3 = xy3 B(2xy)3 = 6x3y3C(3x2)3 = 27x5 D(a2b)n = a2nbn8下列各式錯(cuò)誤的是（ ）A(23)4 = 212 B( 2a)3 = 8a3C(2mn2)4 = 16m4n8 D(3ab)2 = 6a2b29下列計(jì)算中，錯(cuò)誤的是（ ）Amnm2n+1 = m3n+1 B(am1)2 = a 2m2 C(a2b)n = a2nbn D(3x2)3 = 9x6 10下列計(jì)算中，錯(cuò)誤的是（ ）A(2ab2)2( 3a2b)3 = 108a8b7B(2xy)3(2xy)2 = 32x5y5C(m2n)(mn2)2 =m4n4D(xy)2(x2y) = x4y311下列計(jì)算結(jié)果正確的是（ ）A(6ab2 4a2b)3ab = 18ab2 12a2bB(x)(2x+x21) = x32x2+1C(3x2y)(2xy+3yz1) = 6x3y29x2y2z2+3x2yD(a3b)2ab =a4bab212若(x2)(x+3) = x2+a+b，則a、b的值為（ ）Aa = 5，b = 6 Ba = 1，b = 6Ca = 1，b = 6 Da = 5，b = 6二、解答題：1計(jì)算(25)(1). ( 5a3b2)(3ab 2c)( 7a2b)；(2). 2(a5)2(a2)2(a2)4(a2)2a2；(3)(x3)(x3)(x1)(x5) (4). 3a2(ab2b)( 2a2b23ab)( 3a)；(5). (3x25y)(x2+2x3)2當(dāng)x = 3時(shí)，求8x2(x2)(x+1)3(x1)(x2)的值(8)3把一個(gè)長(zhǎng)方形的長(zhǎng)減少3，寬增加2，面積不變，若長(zhǎng)增加1，寬減少1，則面積減少6，求長(zhǎng)方形的面積(7) 參考答案：一、選擇題1.A說(shuō)明： t4與t2不是同類項(xiàng)，不能合并，B錯(cuò)；同底數(shù)冪相乘，底不變，指數(shù)相加，所以t3t4 = t3+4 = t7t12，C錯(cuò)；t5t5 = t5+5 = t102t5，D錯(cuò)；t2t3 = t2+3 = t5，A正確；答案為A2.C說(shuō)明：a2(a)2 = a2a2 = a2+2 = a4，A計(jì)算正確；(a)2(a)4 = a2a4 = a2+4 = a6，B計(jì)算正確；(a3)(a)2 = a3a2 = a5a5，C計(jì)算錯(cuò)誤；(a)(a)2 = aa2 = a3，D計(jì)算正確；所以答案為C3.A說(shuō)明：5x3x3 = (51)x3 = 4x3 x3 ，錯(cuò)誤； 3m與2n 不是同底數(shù)冪，它們相乘把底數(shù)相乘而指數(shù)相加顯然是不對(duì)的，比如m = 1，n = 2，則 3m2n = 3122 = 34 = 12，而 6m+n = 61+2 = 63 = 21612，錯(cuò)誤；am與an只有在m = n時(shí)才是同類項(xiàng)，此時(shí)am+an = 2amam+n，而在mn時(shí)，am與an無(wú)法合并，錯(cuò)；xm+1xm+2 = xm+1+m+2 = xm+m+3 = xmxm+3，正確；所以答案為A4.B說(shuō)明：a6(a2)3 = a6a23 = a6a6 = a6+6 = a12，所以答案為B5.D說(shuō)明：(a3)3 = a33 = a9，A錯(cuò)；(a5)4 = a54 = a20，B錯(cuò)；(a)53 = (a)53 = (a)15 = a15，C錯(cuò)；(a)23 = (a)23 = (a)6 = a6，D正確，答案為D6.D說(shuō)明：(m6)6 = m66 = m36，A計(jì)算正確；(a4)m = a 4m，(a 2m)2 = a 4m，B計(jì)算正確；(xn)2 = x2n，C計(jì)算正確；當(dāng)n為偶數(shù)時(shí)，(x2)n = (x2)n = x2n；當(dāng)n為奇數(shù)時(shí)，(x2)n = x2n，所以D不正確，答案為D7.D說(shuō)明：(xy)3 = x3y3，A錯(cuò)；(2xy)3 = 23x3y3 = 8x3y3，B錯(cuò)；(3x2)3 = (3)3(x2)3 = 27x6，C錯(cuò)；(a2b)n = (a2)nbn = a2nbn，D正確，答案為D8.C說(shuō)明：(23)4 = 234 = 212，A中式子正確；( 2a)3 = (2) 3a3 = 8a3，B中式子正確；(3ab)2 = 32a2b2 = 9a2b2，C中式子錯(cuò)誤；(2mn2)4 = 24m4(n2)4 = 16m4n8，D中式子正確，所以答案為C9.D說(shuō)明：mnm2n+1 = mn+2n+1 = m3n+1，A中計(jì)算正確；(am1)2 = a2(m1) = a 2m2，B中計(jì)算正確； (a2b)n = (a2)nbn = a2nbn，C中計(jì)算正確；(3x2)3 = (3)3(x2)3 = 27x6，D中計(jì)算錯(cuò)誤；所以答案為D10.C說(shuō)明：(2ab2)2( 3a2b)3 = (2) 2a2(b2)2(3)3(a2)3b3 = 4a2b4(27)a6b3 = 108a2+6b4+3 = 108a8b7， A中計(jì)算正確；(2xy)3(2xy)2 = (2xy)3(2xy)2 = (2xy)3+2 = (2xy)5 = 25x5y5 = 32x5y5，B中計(jì)算正確；(m2n)( mn2)2 =m2n() 2m2(n2)2 =m2nm2n4 =m2+2n1+4 =m4n5，C中計(jì)算錯(cuò)誤；(xy)2(x2y) = ()2x2y2x2y =x2y2x2y = x4y3，D中計(jì)算正確，所以答案為C11.D說(shuō)明：(6ab2 4a2b)3ab = 6ab23ab 4a2b3ab = 18a2b3 12a3b，A計(jì)算錯(cuò)誤；(x)(2x+x21) = x2x+(x)x2(x) = 2x2x3+x = x32x2+x，B計(jì)算錯(cuò)誤；(3x2y)(2xy+3yz1) = (3x2y) (2xy)+(3x2y) 3yz(3x2y) = 6x3y29x2y2z+3x2y，C計(jì)算錯(cuò)誤；(a3b)2ab = (a3) 2ab(b)2ab =a4bab2，D計(jì)算正確，所以答案為D12.B說(shuō)明：因?yàn)?x2)(x+3) = xx2x+3x6 = x2+x6，所以a = 1，b = 6，答案為B二、解答題1.解：(1)( 5a3b2)(3ab 2c)( 7a2b) = (5)(3)(7)(a3aa2)(b2b2b)c = 105a6b 5c(2) 2a2b3(mn)5ab2(nm)2+a2(mn)6ab2 = (2)(a2a)(b3b2)(mn)5(mn)2+( 6)(a2a)(mn)b2 = a3b5(mn)7+ 2a3b2(mn)(3) 3a2(ab2b)( 2a2b23ab)( 3a) = 3a2ab2 3a2b+ 2a2b2 3a3ab 3a= a3b2 3a2b+ 6a3b2 9a2b = 7a3b2 12a2b(4)(3x25y)(x2+2x3) = 3x2x25yx2+3x22x5y2x+3x2(3)5y(3)= 3x45x2y+6x310xy9x2+15y= 3x4+6x35x2y9x210xy+15y2. 解：8x2(x2)(x+1)3(x1)(x2) = 8x2(x22x+x2)3(x2x2x+2)= 8x2x2+x+23x2+9x6 = 4x2+10x4當(dāng)x = 3時(shí)，原式 = 4(3)2+10(3)4 = 36304 = 23. 解：設(shè)長(zhǎng)方形的長(zhǎng)為x，寬為y，則由題意有即解得xy = 36答：長(zhǎng)方形的面積是364. 解：(x+my1)(nx2y+3) = nx22xy+3x+mnxy2my2+3mynx+2y3= nx2(2mn)xy2my2+(3n)x+( 3m+2)y3x、y項(xiàng)系數(shù)為0，得故 3m+n = 3()+3 = 1