春七年級(jí)數(shù)學(xué)下冊(cè)第一章整式乘除章末小結(jié)與提升課時(shí)作業(yè)北師大版

第一章整式的乘除章末小結(jié)與提高整式的運(yùn)算種類1冪的運(yùn)算23的結(jié)果是( )典例1計(jì)算(-3x)A.-3x5B.-27x6C.-3x6D.-27x5233236【分析】(-3x)=(-3)·(x)=-27x.【答案】B【針對(duì)訓(xùn)練】1.以下運(yùn)算正確的選項(xiàng)是(A)A.x3·x2=x5B.(x3)3=x6C.x5+x5=x10D.x6-x3=x32.以下運(yùn)算正確的選項(xiàng)是(C)A.-a4·a3=a7B.a4·a3=a12C.(a4)3=a12D.a4+a3=a71種類2整式的乘、除法運(yùn)算典例2計(jì)算:5x2y÷(-xy)×(2xy2)2.【分析】原式=5x2y÷(-xy)×4x2y4=-15x×4x2y4=-60x3y4.【針對(duì)訓(xùn)練】1下邊計(jì)算正確的選項(xiàng)是(C).A.3x2·4x=12x2B.x3·x5=x15C.x4÷x=x3D.(x5)2=x72.xy=7,則x-2y(A)若3=4,93的值為A.B.C.-3D.3.化簡(jiǎn):6a6÷3a3=2a3.4.先化簡(jiǎn),再求值:-2x3y4÷(-x2y2)·(-x)-(x-2y)(3y+x)+x(x+2xy2),此中x=-1,y=-2.解:原式=2xy2·(-x)-(x2-6y2+xy)+x2+2x2y2=-2x2y2-x2+6y2-xy+x2+2x2y2=6y2-xy.當(dāng)x=-1,y=-2時(shí),原式=6×(-2)2-(-1)×(-2)=22.種類3乘法公式1.若a2-b2=,a-b=,則a+b的值為(B)A.-B.C.1D.22.若(7x-a)2=49x2-bx+9,則|a+b|的值為45.3.先化簡(jiǎn),再求值:[(x+2y)(x-2y)-(x+4y)2]÷4y,此中x2-8x+y2-y+16=0.解:x2-8x+y2-y+16=0,2即x2-8x+16+y2-y+=0,則(x-4)2+=0,則x-4=0且y-=0,解得x=4,y=.原式=[x2-4y2-(x2+8xy+16y2)]÷4y=(x2-4y2-x2-8xy-16y2)÷4y=-2x-5y.當(dāng)x=4,y=時(shí),原式=-8-=-.種類4整式的混淆運(yùn)算典例3(邵陽(yáng)中考)先化簡(jiǎn),再求值:(a-2b)(a+2b)-(a-2b)2+8b2,此中a=-2,b=.【分析】原式=a2-4b2-a2+4ab-4b2+8b2=4ab,當(dāng)a=-2,b=時(shí),原式=-4.【針對(duì)訓(xùn)練】1.計(jì)算:(6x4-8x3)÷(-2x2)-(3x+2)(1-x).解:原式=-3x2+4x-3x+3x2-2+2x=3x-2.2.先化簡(jiǎn),再求值:2(x+1)-(x+1)2,此中x=3.3解:原式=2x+2-(x2+2x+1)=2x+2-x2-2x-1=1-x2.當(dāng)x=3時(shí),原式=1-9=-8.3.先化簡(jiǎn),再求值:[(a+b)(a-b)+(a+b)2-2a2]÷2a,此中a=3,b=-.解:原式=(a2-b2+a2+2ab+b2-2a2)÷2a=2ab÷2a=b.當(dāng)a=3,b=-時(shí),原式=-.種類5定義新運(yùn)算41.在實(shí)數(shù)范圍內(nèi)定義運(yùn)算“☆”,其規(guī)則為a☆b=a2-b2,則方程(4☆3)☆x=13的解為x=±6.2.現(xiàn)規(guī)定一種新的運(yùn)算“※”:a※b=ba,如3※2=23=8,求4※和3※(-a2b).解:4※,3※(-a2b)=(-a2b)3=-a6b3.種類6規(guī)律研究1.依據(jù)以低等式:1=12,21+2+1=2,21+2+3+2+1=3,關(guān)于正整數(shù)n(n≥4),猜想1+2++(n-1)+n+(n-1)++2+1=n2.2.察看以下各式:3×5=15,15=42-1,5×7=35,35=62-1,511×13=143,