2026北师大七年级数学上举一反三：专题3.2 整式(讲义)(原卷版)

专题3.2整式（举一反三讲义）



2024



1

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2

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3!"#

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4!"#$

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5%#&'()

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6*!"

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7+#,-.'/012034

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8*56789

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知识点1单项式

1.

<=>.?@1'(ABCDE.?FGHI>.1>.'(J@

H

2.

5'LFGE.H

3.

>.5BNO'(PQFGE.HRS>.TUB6

VW0H

知识点2多项式

1.

Y.QFG#H

2.#

Z#5B[.FG#B\5]^'(FG_B>.#^

OYB`FYH

3.#

#aBbcBFGE.#H

知识点3整式

1.

$#de*H

2.#$*<fNgH

3.!"*h#ij

k1l]^mnopB#q^mnopr

k2l#@Y.QB#]s^r

k3lQ#t@*Bu(5^O'(t]@*H

【题型1单项式的定义】

v

kwxyz{|}~l€4?B5B.O

124-25··8+2

222푥−1

kl푎2,−푥푦,3푎,0,푏,

AH3.BH4.CH5.DH6.

1-1

k24-25wxyz·‚ƒ‚„·~l€4?5B…S@kl

1

HHHH

A6BC+D2

푥푠푥+

푡3푥2푦

1-2

k24-25wxy€·†‡‡„·ˆ‰Š‹lZ1BB20%B4+8=12B

4

22

1①푥②푎−푏③푥④

B5B…SOH

3

푚−푛

⑤⑥푎2

1-3

k24-25wxyz·ŒŽ·~5l€4?

rmr3rrr

343

22푥+3푦푎푏

①②③푥푦④⑤푚

+rB\5@@k‘’lH

푥

⑥6푥3푦⑦휋

【题型2单项式的系数、次数】

v2

k24-25wxyz·“”·~5l•–>.@3B@4B—E.˜™@kl

AHBHCH3+DH3

2423

1

3푥2-1푦

k24-25wxyz−3푥·š›œ·~l€4

푥푦푥푦,,5BžO

3

2푎3

푥

.rW1@rW@−푚,0,r(−1)푥푦푧,2휋푅,−푥@H

2

2-2

k24-25wxyz·Ÿ

¡·−1~5l¢>.£¤¥¦§¨

(−1)푥푦푧^O'(xByBzr

WrW5B—E©žOkl①②

−3③

AH5.BH6.CH7.DH8.

1

2-3

k24-25wxy€·Ÿª«¬·­

®¯l@rt@

2222

π푥

34①−−②푎푏

r$t@r@H™z°j5±²Ok³³l

1422

A③H0.푎B④H1.π푟CHπ2.DH3.

【题型3判断多项式】

v3

k24-25wxyz·Œ{´·~lZ?+2(+1),25B#.@kl

푥+푦푚+푛

.−1,2푥7,−π,푥푥

AH5BH4CH3DH2

131

3-1

Z?r+;B2+15B€4!"±²@kl

22

푛

AH@①BH푥푦@µ②푎¶−푎푏푏③CH④푥@#DH@*

①③3-2

€4°j±²@k②l②④①④

AHBB+B3t@*BH2Q2t@

2푥−1푥+푦푥푦

푎1−6푎푏푐

CHQ++t@#DH@Q1

푦+22

푦푥푥푦푦3푥−13푥

1222



€4*﹣xy，42，x+y﹣1，﹣5，x，2﹣y5Oa.Bb.#B—ab＝．

3-327

푚푛

【题型4判断多项式的项与次数】

1

v

kwxyz·¸ª¹~5l@B_@B—)@H

424-25··2+

232

4-1

k24-25ºxy€·z»·~5l€4#5@¶푥푦−푥푦푥푦−3¶@k푎l푏푎푏

AH3rBHrCH+rDH+H

22

4-2푥

k24-25wxyz푥푦−3푦−1·{¼½·ˆ‰Š‹l푥푦−32푥푦+1+4푥bc푥푦−3푦@H

5

33

−2푎푏푎푏−3푏

4-3

k24-25wxyz·z»¾œ·~5l#102bc@H

3푎푏−2푎푏+

【题型5由多项式的系数、次数求字母的值】

v5

<=#5()+1@SaµµB+=H

푚

5-1

k24-25wxyz푎−푛−1·¿À푎·~l•–S#(푚2푛)+Wµ¶B—Á

3푛

=¤BE.µ¶)@H푥푚−4푥−푥푥−푚푛

푥−15-2

•–(+10)++5@Sµ#BÂÃBB¥¦()=|+|B

322

푎푥푐푥−2푥푥푎푏푐푐−18−푎푏

—+=H

푎−푏5-3푐

k24-25wxyz··¸ª¹·~5lS#||+3W3BWÄ)

푎+453

kl푥푎푥−푥푥−5푎

AH0BH1CHDH±1

−1

【题型6整式的判断】

1

v6

€4

+2B+4B72BBB05B*.@k³³l

23푎푏푎푏

AH3푥BH4푎푐5푥CH5DH6

1

6-1

€4

①+1r②+r③++2r④r⑤H\5#O

22422

.Bbc#W푥−푥kőƒlB*O푚푛푚푛−1푥.H푥5−푥−푥

1

6-2

?、、、0、、、3+、+、、+5BO

22푎푥

푥푎

.B#O2푥−푦.B*O푚푥−푥푦.．−푎푏푏2(푎푏)|−0.5|푦

2

6-3

ÇȀ4É

B2BB+B+HÊˀ4Ì

푎2

(1)uÍW

______________________________−푎푏−푎푎푏푎r푎−1

(2)#uÍW

_________________________________r

(3)*O___________.r

(4)W__________r

(5)−푎푏bc#W__________________H

【题型7将多项式按某个字的升幂或降幂排列】

v7

k24-25wxyz·z»ÎÏ·~l+*3+2+,2034ÐBѵ

7푚+14푚236

WH푥푦−4푥푦푥푦푥푦푦

7-1

k24-25wxyz·z»ÒÓ·ˆ‰Š‹l#3-2xy+6xy-5xy-4xy@,Ô().

2324

AH,'(x/034BH,'(y/034

CH,'(x2034DH,'(y2034

7-2

k2025·{ªÕ„·>ÖlÆ×>.£¤¥¦€4§¨µ¶

^O'(Qr[>t@2r,'(2034H

①7-3

k푎24-25푏wxyz②·z»ØÙ·ˆ‰Š‹l-#W③푎++B,E©67

876253

ƀÚBÑ6@BÛ#Ü@H푥−푥푦푥푦−푥푦⋯

【题型8整式中的规律探究】

v8

k24-25Ýxy€·Þªßà·~5lÇȀ4

B+4BB+16B…

234

Åáâ×\567Bã+Ñ푥−1푥푥−9푥.Æ×ä

H

푛

8-1

k24-25wxyz·Þªßà·~5l,Ô>6734BBBB…B¯åæÑ

2436587

푥푥푥푥

.Wkl푛

AHBHCHDH

2푛+1