七年级数学下册8.4.2单项式与多项式相乘同步练习新版冀教版.docx

8.4.2 单项式与多项式相乘基础训练1.计算2x(3x2+1),正确的结果是()A.5x3+2x B.6x3+1 C.6x3+2x D.6x2+2x2.计算2a(-3a3-2a2-1)的结果是()A.-6a4-4a3-2a B.-6a4+4a3-2aC.-6a4-4a3+2a D.-6a4+4a3+2a3.已知x2-2=y,则x(x-3y)+y(3x-1)-2的值是()A.-2 B.0 C.2 D.44.若一个三角形的底边长为2x2y+xy-y2,高为6xy,则这个三角形的面积是()A.6x3y2+3xy-3xy3 B.6x3y2+3x2y2-3xy3C.6x3y2+3x2y2-y2 D.6x3y+2y25.计算:a(a+1)=_.6.计算:(1)-3x(2x2-3x+1);(2)-2a2b(abc-ab2-1);(3)3xy;(4)(-4xy2);(5)xy(2x-y)-2x(xy-y2).培优提升1.(-3x+1)(-2x)2等于()A.-6x3-2x2B.6x3-2x2 C.6x3+2x2 D.-12x3+4x22.当a=4,b=2,c=12时,a(b-c)-b(c-a)+c(a-b)的值为()A.5B.10 C.12D.143.下列计算正确的是()A.xn(xn-x2+3)=x2n-xn+2+3xnB.(2x+3y)(-4xy)=-8x2y-12xy2=-20xyC.(-2xy2-4x2y)(-3xyz)=6x2y3+12x3y2D.(xyz-7x2y+1)(-xz)=-x2yz2+7x3yz4.现规定一种运算:a*b=ab+a-b,其中a,b为有理数,则a*b+(b-a)*b等于()A.a2-b B.b2-b C.b2 D.b2-a5.若-2x2y(-xmy+3xy3)=2x5y2-6x3yn,则m=_,n=.6.计算下列各题:(1);(2)2ab(a2b2-ab+1)+3ab(1-ab).7.先化简,再求值:3(2x+1)+2(3-x),其中x=-1.8.已知ab2=-1,求(-ab)(a2b5-ab3-b)的值.9.已知-2m2(3m2-pm-6)-3m3+m2中不含m3项,试确定p的值.10.一张长方形硬纸片,长为(5a2+4b2)m,宽为6a4 m,若在它的四个角上分别剪去一个边长为32a3 m的小正方形,然后折叠成一个无盖的盒子,求这个无盖的盒子的表面积.参考答案【基础训练】1.【答案】C 2.【答案】A3.【答案】B解：x(x-3y)+y(3x-1)-2化简后的结果是x2-y-2,由x2-2=y可得x2-y-2=0.4.【答案】B5.【答案】a2+a6.解:(1)-3x(2x2-3x+1)=-6x3+9x2-3x. (2)-2a2b(abc-ab2-1)=-2a2babc+(-2a2b)(-ab2)+(-2a2b)(-1)=-2a3b2c+2a3b3+2a2b.(3)3xy=3xy3xy+32x2y=9x2y2+92x3y2.(4)(-4xy2)=-3x3y3+2x2y4+103xy5.(5)xy(2x-y)-2x(xy-y2)=19x2y2(2x2y-xy2-2x2y+2xy2)=19x2y2xy2=19x3y4.【培优提升】1.【答案】D解：先算乘方,再运用多项式与单项式的乘法法则计算.2.【答案】D 3.【答案】A4.【答案】B解：解答本题的关键是理解规定的运算,并计算出(b-a)*b,对照规定的运算,应把b-a看成一个整体,可得(b-a)*b=(b-a)b+(b-a)-b=b2-ab+b-a-b=b2-ab-a,所以a*b+(b-a)*b=ab+a-b+ b2-ab-a=b2-b.故选B.5.【答案】3;4解：-2x2y(-xmy+3xy3)=2xm+2y2-6x3y4=2x5y2-6x3yn,m+2=5,n=4,m=3,n=4.6.解:(1)原式=14x2y2=14x2y243x2y-14x2y28xy2+14x2y25x-14x2y2=13x4y3-2x3y4+54x3y2-14x2y2;(2)原式=2aba2b2-2abab+2ab+3ab-3abab=2a3b3-2a2b2+5ab-3a2b2=2a3b3-5a2b2+5ab.7.解:原式=6x+3+6-2x=4x+9.当x=-1时,原式=4(-1)+9=5.8.解:原式=-a3b6+a2b4+ab2=-(ab2)3+(ab2)2+ab2=-(-1)3+(-1)2+(-1)=1.9.解:-2m2(3m2-pm-6)-3m3+m2=-6m4+2pm3+12m2-3m3+m2=-6m4+(2p-3)m3+13m2,由题意可知2p-3=0,p=32.10.解:这个无盖的盒子的表面积为: