整式的除法課件～北師大版數(shù)學(xué)七年級(jí)下冊(cè)

4整式的除法2024～2025學(xué)年北師大版數(shù)學(xué)七年級(jí)下冊(cè)課時(shí)目標(biāo)素養(yǎng)達(dá)成1.理解單項(xiàng)式除以單項(xiàng)式、多項(xiàng)式除以單項(xiàng)式的運(yùn)算法則運(yùn)算能力、應(yīng)用意識(shí)2.會(huì)進(jìn)行單項(xiàng)式除以單項(xiàng)式、多項(xiàng)式除以單項(xiàng)式的整式除法運(yùn)算抽象能力、推理能力1.計(jì)算6x3÷3x2的結(jié)果是()A.x

B.2x

C.2x5

D.2x62.計(jì)算(25x2y-5xy2)÷5xy的結(jié)果等于()A.-5x+y

B.5x-y

C.-5x+1 D.-5x-13.計(jì)算:(-9x2+3x)÷(-3x)=_________.

BB

3x-1

單項(xiàng)式除以單項(xiàng)式(運(yùn)算能力)【典例1】(教材再開發(fā)·P27例補(bǔ)充)計(jì)算:(1)(2024·廣州白云期中)(-2x2y3)3÷(-x2)2.(2)7.2×1012÷(-3.6×109).【自主解答】(1)原式=-8x6y9÷x4=-8x2y9.(2)原式=[7.2÷(-3.6)]×(1012÷109)=-2×103.1.(2024·深圳龍華質(zhì)檢)25x2y3÷(-5xy)的運(yùn)算結(jié)果是()A.-5x2y

B.5xy2C.5x2y

D.-5xy2【解析】25x2y3÷(-5xy)=-5xy2.D2.(2024·珠海十一中一模)計(jì)算:8x3y÷(2x)2=________.

【解析】原式=8x3y÷4x2=2xy.

2xy

多項(xiàng)式除以單項(xiàng)式(運(yùn)算能力)【典例2】(教材再開發(fā)·P28習(xí)題T1補(bǔ)充)計(jì)算:(1)(2024·河源龍川期末)[(2a)2-4ab+2a]÷2a.(2)計(jì)算:(12m4n-9m2n2+3m3)÷(-3m2).【自主解答】(1)原式=(4a2-4ab+2a)÷2a=2a-2b+1.(2)原式=12m4n÷(-3m2)-9m2n2÷(-3m2)+3m3÷(-3m2)=-4m2n+3n2-m.1.(2024·茂名電白期中)(10x2y-5xy2)÷(-5xy)的結(jié)果是()A.2x+y

B.2x-yC.-2x-y

D.-2x+y【解析】(10x2y-5xy2)÷(-5xy)=10x2y÷(-5xy)-5xy2÷(-5xy)=-2x+y.D2.一個(gè)長方形的面積是xy2-x2y,若長為xy,那么寬為()A.x-y

B.y-x

C.x+y

D.-x-y【解析】長方形的寬為:(xy2-x2y)÷xy=xy2÷xy-x2y÷xy=y-x.B

1.(2024·佛山順德質(zhì)檢)計(jì)算(-4x3+2x)÷2x的結(jié)果正確的是()A.-8x4+4x2

B.-4x3C.-2x

D.-2x2+1【解析】(-4x3+2x)÷2x=-2x2+1.D

3.計(jì)算:(1)(2024·深圳南山質(zhì)檢)(-3xy2)2·(-6x2y)÷(9x4y5).(2)[(3a-b)2+(a+b)(a-b)]÷2a.【解析】(1)原式=9x2y4·(-6x2y)÷(9x4y5)=-54x4y5÷(9x4y5)=-6.(2)原式=(9a2-6ab+b2+a2-b2)÷2a=(10a2-6ab)÷2a=5a-3b.知識(shí)點(diǎn)1

單項(xiàng)式除以單項(xiàng)式1.計(jì)算-14x3y3÷7x2y的結(jié)果是()A.2x

B.-2x C.2y2

D.-2xy2【解析】原式=[(-14)÷7]·(x3÷x2)·(y3÷y)=-2xy2.D2.已知28a3bm÷(28anb2)=b2,那么m,n的值分別為()A.4,3 B.4,1

C.1,3

D.2,3

A知識(shí)點(diǎn)2

多項(xiàng)式除以單項(xiàng)式3.計(jì)算(x3-2x2y)÷(-x2)的結(jié)果是()A.x-2y

B.-x+2yC.-x-2 D.-x+2【解析】原式=x3÷(-x2)-2x2y÷(-x2)=-x+2y.B4.(2024·清遠(yuǎn)英德期中)計(jì)算:(9a3b2-3ab)÷3ab=__________.

【解析】原式=9a3b2÷3ab-3ab÷3ab=3a2b-1.

3a2b-1

5.計(jì)算:(12m4n-9m2n2+3m3)÷(-3m2).【解析】(12m4n-9m2n2+3m3)÷(-3m2)=12m4n÷(-3m2)-9m2n2÷(-3m2)+3m3÷(-3m2)=-4m2n+3n2-m.知識(shí)點(diǎn)3

整式的混合運(yùn)算6.計(jì)算[(-a2)3-3a2(-a2)]÷(-a)2的結(jié)果是()A.-a3+3a2 B.a3-3a2C.-a4+3a2 D.-a4+a2【解析】原式=(-a6+3a4)÷a2=-a4+3a2.C7.[(x+y)2-(x-y)2]÷4xy=______.

【解析】[(x+y)2-(x-y)2]÷4xy=[x2+2xy+y2-(x2-2xy+y2)]÷4xy=(x2+2xy+y2-x2+2xy-y2)÷4xy=4xy÷4xy=1.

1

8.(2024·汕尾陸河質(zhì)檢)計(jì)算:(2y-x)(x-y)+(2x3y+4xy3)÷2xy.【解析】原式=2xy-2y2-x2+xy+x2+2y2=3xy.9.計(jì)算4a·3a2b÷2ab的結(jié)果是()A.6a

B.6ab

C.6a2

D.6a2b2【解析】4a·3a2b÷2ab=12a3b÷2ab=6a2.C10.(2024·連州市期末)若長方形的面積是8a3+12a2-4ab,其中一邊長是4a,則它的鄰邊長是()A.2a3+3a2-b

B.2a2+3a+bC.3a2+2a+b

D.2a2+3a-b【解析】由題意得:(8a3+12a2-4ab)÷4a=8a3÷4a+12a2÷4a-4ab÷4a=2a2+3a-b,所以長方形的鄰邊長是2a2+3a-b,所以A,B,C選項(xiàng)均不符合題意,D選項(xiàng)符合題意.D11.某興趣小組的門鎖密碼被設(shè)計(jì)成如表所示的數(shù)學(xué)問題,正確的密碼是_________.

[x19y8z8]=1988[x2yz·x3y]=521[(x5)5y4z6÷x5y2z]=密碼【解析】因?yàn)閇(x5)5y4z6÷x5y2z]=[x25y4z6÷x5y2z]=[x20y2z5],已知:x,y,z的指數(shù)是密碼,所以密碼為2025.

2025

12.先化簡,再求值:(2m+3)(2m-3)-(m-1)2+(2m)3÷(-8m),其中m滿足m2+m-2=0.【解析】原式=4m2-9-(m2-2m+1)+8m3÷(-8m)=4m2-9-m2+2m-1-m2=2m2+2m-10=2(m2+m)-10,因?yàn)閙2+m-2=0,所以m2+m=2,所以原式=2×2-10=-6.13.(2024·佛山禪城質(zhì)檢)觀察下列式子:(x2-1)÷(x-1)=x+1(x3-1)÷(x-1)=x2+x+1(x4