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1、151整式的乘法习题精选选择题：1下列各式中，正确的是( )At2t3 = t5 Bt4+t2 = t 6 Ct3t4 = t12 Dt5t5 = 2t5答案：A说明：t4与t2不是同类项，不能合并，B错；同底数幂相乘，底不变，指数相加，所以t3t4 = t3+4 = t7t12，C错；t5t5 = t5+5 = t102t5，D错；t2t3 = t2+3 = t5，A正确；答案为A2下列计算错误的是( )Aa2(a)2 = a4 B(a)2(a)4 = a6C(a3)(a)2 = a5 D(a)(a)2 = a3答案：C说明：a2(a)2 = a2a2 = a2+2 = a4，A计算正确；(
2、a)2(a)4 = a2a4 = a2+4 = a6，B计算正确；(a3)(a)2 = a3a2 = a5a5，C计算错误；(a)(a)2 = aa2 = a3，D计算正确；所以答案为C3下列计算中，运算正确的个数是( )5x3x3 = x3 3m2n = 6m+nam+an = am+n xm+1xm+2 = xmxm+3A1 B 2 C3 D4答案：A说明：5x3x3 = (51)x3 = 4x3 x3 ，错误； 3m与2n 不是同底数幂，它们相乘把底数相乘而指数相加显然是不对的，比如m = 1，n = 2，则 3m2n = 3122 = 34 = 12，而 6m+n = 61+2 = 6
3、3 = 21612，错误；am与an只有在m = n时才是同类项，此时am+an = 2amam+n，而在mn时，am与an无法合并，错；xm+1xm+2 = xm+1+m+2 = xm+m+3 = xmxm+3，正确；所以答案为A4计算a6(a2)3的结果等于( )Aa11 Ba 12 Ca14 Da36答案：B说明：a6(a2)3 = a6a23 = a6a6 = a6+6 = a12，所以答案为B5下列各式计算中，正确的是( )A(a3)3 = a6 B(a5)4 = a 20 C(a)53 = a15 D(a)23 = a6答案：D说明：(a3)3 = a33 = a9，A错；(a5)
4、4 = a54 = a20，B错；(a)53 = (a)53 = (a)15 = a15，C错；(a)23 = (a)23 = (a)6 = a6，D正确，答案为D6下列各式计算中，错误的是( )A(m6)6 = m36 B(a4)m = (a 2m) 2 Cx2n = (xn)2 Dx2n = (x2)n答案：D说明：(m6)6 = m66 = m36，A计算正确；(a4)m = a 4m，(a 2m)2 = a 4m，B计算正确；(xn)2 = x2n，C计算正确；当n为偶数时，(x2)n = (x2)n = x2n；当n为奇数时，(x2)n = x2n，所以D不正确，答案为D7下列计算正
5、确的是( )A(xy)3 = xy3 B(2xy)3 = 6x3y3C(3x2)3 = 27x5 D(a2b)n = a2nbn答案：D说明：(xy)3 = x3y3，A错；(2xy)3 = 23x3y3 = 8x3y3，B错；(3x2)3 = (3)3(x2)3 = 27x6，C错；(a2b)n = (a2)nbn = a2nbn，D正确，答案为D8下列各式错误的是( )A(23)4 = 212 B( 2a)3 = 8a3C(2mn2)4 = 16m4n8 D(3ab)2 = 6a2b2答案：C说明：(23)4 = 234 = 212，A中式子正确；( 2a)3 = (2) 3a3 = 8a
6、3，B中式子正确；(3ab)2 = 32a2b2 = 9a2b2，C中式子错误；(2mn2)4 = 24m4(n2)4 = 16m4n8，D中式子正确，所以答案为C9下列计算中，错误的是( )Amnm2n+1 = m3n+1 B(am1)2 = a 2m2C(a2b)n = a2nbn D(3x2)3 = 9x6 答案：D说明：mnm2n+1 = mn+2n+1 = m3n+1，A中计算正确；(am1)2 = a2(m1) = a 2m2，B中计算正确； (a2b)n = (a2)nbn = a2nbn，C中计算正确；(3x2)3 = (3)3(x2)3 = 27x6，D中计算错误；所以答案为
7、D10下列计算中，错误的是( )A(2ab2)2( 3a2b)3 = 108a8b7B(2xy)3(2xy)2 = 32x5y5C(m2n)(mn2)2 =m4n4D(xy)2(x2y) = x4y3答案：C说明：(2ab2)2( 3a2b)3 = (2) 2a2(b2)2(3)3(a2)3b3 = 4a2b4(27)a6b3 = 108a2+6b4+3 = 108a8b7，A中计算正确；(2xy)3(2xy)2 = (2xy)3(2xy)2 = (2xy)3+2 = (2xy)5 = 25x5y5 = 32x5y5，B中计算正确；(m2n)(mn2)2 =m2n() 2m2(n2)2 =m2
8、nm2n4 =m2+2n1+4 =m4n5，C中计算错误；(xy)2(x2y) = ()2x2y2x2y =x2y2x2y = x4y3，D中计算正确，所以答案为C11下列计算结果正确的是( )A(6ab2 4a2b)3ab = 18ab2 12a2bB(x)(2x+x21) = x32x2+1C(3x2y)(2xy+3yz1) = 6x3y29x2y2z2+3x2yD(a3b)2ab =a4bab2答案：D说明：(6ab2 4a2b)3ab = 6ab23ab 4a2b3ab = 18a2b3 12a3b，A计算错误；(x)(2x+x21) = x2x+(x)x2(x) = 2x2x3+x
9、= x32x2+x，B计算错误；(3x2y)(2xy+3yz1) = (3x2y) (2xy)+(3x2y) 3yz(3x2y) = 6x3y29x2y2z+3x2y，C计算错误；(a3b)2ab = (a3) 2ab(b)2ab =a4bab2，D计算正确，所以答案为D12若(x2)(x+3) = x2+a+b，则a、b的值为( )Aa = 5，b = 6 Ba = 1，b = 6Ca = 1，b = 6 Da = 5，b = 6答案：B说明：因为(x2)(x+3) = xx2x+3x6 = x2+x6，所以a = 1，b = 6，答案为B解答题：1计算(1)( 5a3b2)(3ab 2c)
10、( 7a2b)；(2) 2a2b3(mn)5ab2(nm)2+a2(mn)6ab2；(3) 3a2( ab2b)( 2a2b23ab)( 3a)；(4)(3x25y)(x2+2x3)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
11、+ 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当x = 3时，求8x2(x2)(x+1)3(x1)(x2)的值解：8x2(x2)(x+1)3(x1)(x2) = 8x2(x22x+x2)3(x2x2x+2)= 8x2x2+x+23x2+9x6 = 4x2+10x4当x = 3时，原式 = 4(3)2+10(3)4 = 36304 = 23把一个长方形的长减少3，宽增加2，面积不变，若长增加1，宽减少1，则面积减少6，求长方形的面积解：设长方形的长为x，宽为y，则由题意有即解得xy = 36答：长方形的面积是364(x+my1)(nx2y+3)的结果中x、y项的系数均为0，求 3m+n之值解：(x+my1)(nx2y+3) = nx22xy+3x+mnxy2my2+3mynx+2y3= nx2(2mn)xy2my2+(3n)x+( 3m+2)y3x、y项系数为0，得故 3m+n = 3()+3 = 1