dai so 8 3 cot cuc hot
TRANSCRIPT
Ngy son: 27/8/04
Gio n: i S 8 Nm hc 2011 - 2012
Tun: Ngy son: Ngy dy:
Lp:
Tit :1 Chng 1: PHP NHN V PHP CHIA CAC A THC1 NHN N THC VI A THCI / MC TIU:
- Kin thc: HS nm c quy tc nhn n thc vi a thc.- K nng: K nng thu gn n thc nhanh khi lm bi tp.Bit vn dng quy tc linh hot gii ton.
- Thi : Rn luyn tnh cn thn, chnh xc trong tnh ton.
II / CHUN B:
-Thy: Gio n, phn mu.
-HS : n php nhn phn phi vi php cng n thc, a thc . III/ TIN TRNH TIT DY:1. n nh:GV nm s s, tnh hnh hc tp v cn b lp.
2. Kim tra:GV kim tra dng hc tp ca HS. Nu mt s yu cu phc v cho vic hc Ton lp 8.
3. Bi mi:
Hot ng ca ThyHot ng ca TrGhi bng
Gii thieu bai mi
GV gii thiu s lc v chng trnh i s 8.
Cho HS nhc li:
+Quy tc nhn mt s vi mt tng, ghi di dng cng thc(GV ghi gc bng).
+Quy tc nhn hai lu tha cng c s: xm.xn = ?
+Quy tc nhn cc n thc?
Mun nhn mt n thc vi a thc ta lm th no? GV gii thiu bi mi.+HS tr li:....
a(b+c) = ab+ac
+ HS tr li:...
xm.xn = xm+n
+ HS tr li...
Qui tac+Cho HS lm ?1
-Hy cho mt v d v n thc?
-Hy cho mt v d v a thc?
-Hy nhn n thc vi tng hng t ca a thc?
-Hy cng cc kt qu tm c.
(Gi HS tr li ming,GV ghi bng ng thi hng dn cch ghi.
+Qua bi tp trn, cho bit: mun nhn mt n thc vi mt a thc ta lm th no?
-GV gii thiu quy tc.
- Gi HS nhc li.HS thc hin, chng hn:
+n thc: 3x.
+a thc: 2x2-2x+5.
+HS thc hin: nhn....., cng... c kt qu:
3x(2x2-2x+5) = =3x.2x2+3x.(-2x)+3x.5
=6x3-6x2+15
+HS tr li...
HS nhc li quy tc.1/Quy tc:
?1: (SGK)
* Quy tc : (SGK T4)
p dng
+Hy p dng quy tc tnh tch sau: (-5x2) (2x3- x + )
-Gi mt i din ln bng
-GV kim tra vi nhm
-Gi HS nhn xt-HS thc hin nhm.
-Mt i din nhm ln bng
Cc nhm nhn xt bi gii2/p dng:
V d: lm tnh nhn:
(-5x2)(2x3- x + )
=(-5x2)2x3+(-5x2) (-x) +(-5x2)
= -10x5+5x3-2x2
+GV: Da vo nh ngha a thc v bi tp trn,ta c th din t ni dung quy tc trn nh sau:
A.(B+C) = A.B +A.C
+Cho hc sinh lm ?2
-Gi HS nhn dng biu thc.
-Ta thc hin nhn nh th no?
- Cho 1 HS ln bng lm
+GV xem mt s bi lm ca HS sau nhn xt v sa sai (nu c) (kq:18x4y4-3x3y3+x2y4)+GV lu : cch nhn n thc vi a thc v nhn a thc vi n thc l nh nhau. Ta c:
A.(B+C) = (B+C).A
+Cho hc sinh lm ?3-Gi HS c .
-Gi HS thc hin yu cu 1 (nu HS khng thc hin c, cho HS nhc li cng thc tnh S hnh thang)
-Gi HS thc hin yu cu tip theo.
+GV: Bi tp ?3 c dng tnh gi tr ca biu thc.
Ta thc hin th no?
- HS: lng nghe
-HS:... nhn n thc vi a thc
-HS:...s dng tnh cht giao hon ca php nhn, nh vy ta nhn n thc vi a thc
-HS ln bng lm:
-HS nhn xt:...
-HS: c .
a) Din tch mnh vn c tnh theo x v y nh sau:
S=
= (8x+3+y).y
S = 8xy+3y+y2
b) Nu x = 3 m; y = 2 m th S ca mnh vn l:
8.3.2+3.2+22=...= 58(m2)
-HS tr li:...Vit biu thc, p dng nhn n thc vi a thc, ri thu gn.
* Thay Gi tr ca x v y vo biu thc thu gn ri tnh
?2: (SGK)
?3: (SGK)
4. Cng c:
Hot ng ca ThyHot ng ca TrGhi bng
+GV cho HS lm 1c (SGK)
+GV cho HS lm bi 3a(SGK)
Hng dn: thc hin php nhn, thu ri ri tm x.
-Gi HS ln bng.
-GV nhn xt , sa sai.- HS ln bng thc hin:
- HS ln bng thc hin3x(12x 4) 9x(4x 3) = 3036x2 12x 36x2 + 27x = 30
15x = 30
x = 2* BT1C (SGK t5)
* BT3a (SGK t5)
5. Hng dn t hc : - Hc thuc quy tc. - Gii cc bi tp: 4, 5, 6 (SGK)
- BTLT: Tnh gia tr cua bieu thc:P(x)= x7-80x6+80x5-80x4+.+80x+ 15 vi x =79
IV/ RT KINH NGHIM TIT DY :..........................................................................................................................................................................................................................................................................................................................
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Tun: Ngy son:
Ngy dy:
Lp: Tit 2 2 NHN A THC VI A THC I. MC TIU: - Kin thc: HS nm vng quy tc nhn a thc vi a thc .- K nng: HS bit trnh by php nhn a thc theo cc cch khc nhau.HS c pht trin t duy, nng lc khi qut ha.
- Thi : HS c rn luyn tnh cn thn, chnh xc, kin tr, vt kh.
II. CHUN B:
-Thy: Gio n, bng ph ghi bi, ghi cc bc nhn a thc v ghi ?3. -HS: n quy tc nhn n thc vi a thc, gii bi tp v nh.
dng hc tp.III. TIN TRNH TIT DY:1. n nh: Nm s s HS, n nh lp.2. Kim tra bi c: Hot ng ca ThyHot ng ca Tr
GV gi 1 HS ln bng ?
-Pht biu quy tc nhn n thc vi a thc.
- p dng gii bi tp 1 a(kq: a) 5x5-x3-x2- GV nhn xt bi lm ca HS v cho im.1 HS ln bng:- Pht biu quy tc nh SGK
- p dng
3. Bi mi: GV gii thiu bi: tit hc trc ta bit cch nhn n thc vi a thc vy cn nhn a thc vi a thc th phi lm th no ta s cng nhau nghin cu Quy tc nhn trong tit hc ny.
Hot ng ca ThyHot ng ca TrNi dung bi
Quy tac+GV hng dn HS thc hin v d:
Cho hai a thc x-2 v 5x2+2x-1
-Hy nhn mi hng t ca a thc x-2 vi tng hng t ca a thc 5x2+2x-1
(thc hin 2 bc)
-Hy cng cc kt qu tm c
GV nhc nh HS ch du ca cc hng t
+GV: Ta ni a thc 5x3-8x2-5x+2 l tch ca a thc x-2 v a thc 5x2+2x-1
-Qua v d trn, hy cho bit mun nhn a thc vi a thc ta lm th no? Ri GV gii thiu quy tc.
-Gi HS nhc li quy tc.
-GV lu HS tch ca hai a thc l mt a thc .
+ Cho HS lm ?1
- GV gi 1 HS ln bng trnh by v xem vi bi lm ca HS cn li, sau nhn xt v sa sai nu c.
-GV lu HS c th rt bt bc nhn mi hng t ca a thc th nht vi a thc th hai
+ GV gii thiu phn ch :
-GV a bng ph ghi php ton trn bng v hng dn HS thc hin nhn hai a thc sp xp.
-Em no c th pht biu cch nhan 2 a thc qua v d trn?
-GV: y chnh l cch nhn hai a thc sp xp.
-Cho HS nhc li cch trnh bi theo SGKHS lng nghe v lm theo hng dn ca GV
-C lp cng thc hin.
-HS ng ti ch tr li ming.
-Mt HS tr li ming
-HS tr li:...
-Hai HS nhc li quy tc.
-HS ln bng trnh by:
-HS tr li:...
-
HS c SGK:...
1/Quy tc:
a)V d:
(x-2) (5x2+2x-1)
= x(5x2+2x-1)-
-2(5x2+2x-1)
=5x3+2x2-x-10x2-4x + 2
=5x3-8x2-5x+2.
b)Quy tc:
(xem SGK trg 7)
* NX: (SGK)
?1 (SGK t7)
*Ch : Khi nhn cc a thc mt bin ta sp xp a thc theo lu tha gim ca bin ri thc hin theo ct dc.
-Cch thc hin:
(Xem SGKtrg 7)
Ap dung
+Cho HS lm ?2.
-Cho HS gii bi theo nhm, yu cu gii cu a) theo 2 cch, mi dy thc hin 1 cch.
-Gi 2 i din ln bng, GV kim tra mt s nhm.
-Cho HS nhn xt, sa sai.
-Cho HS gii bi b)
*Lu HS bi ny a thc cha nhiu bin, nn khng nn tnh theo ct dc.
-Gi 1HS ln bng
-GV kim tra mt s nhm. Cho HS nhn xt, sa sai.
+Cho HS lm ?3
-Gi HS c .
-Gi HS vit biu thc tnh S hnh ch nht
*GV lu HS thu gn biu thc.
-Gi 1 HS tnh S khi:
x = 2,5m v y = 1m.
*GV lu , nn vit x = 2,5 = khi thay vo tnh s n gin hn.-HS thc hin theo nhm.
-2 i din ln bng gii cu a theo 2 cch.
-HS nhn xt bi lm ca bn.
-HS lm bi vo v.
-HS ln bng thc hin.
-HS nhn xt bi lm ca bn.
-HS ln bng thc hin.
a)Biu thc tnh S hnh ch nht l:
(2x+y) (2x-y)
=...
= 4x2-y2
b) Khi x = 2,5m v y = 1m th S hnh ch nht l:
4.()2-12=25-1 =24m2.2/ p dng:
?2: (SGK)
-Lm tnh nhn:
a)(x+3)(x2+3x-5)
=...
= x3+6x2+4x-15
b) (xy-1) (xy+5)
= ...
= x2y2+4xy-5.
-Thc hin ?3
4. Cng c:Hot ng ca ThyHot ng ca TrNi dung bi
Cng c:
Cho HS lm bi tp 7
-GV sa sai, trnh by bi gii hon chnh.
-HS lm bi.-HS lm bi vo v.
(kq:7a) x3- 3x2+3x -1 7b) x4+7x3-11x2
+6x-5
kt qu suy t cu b)
x4-7x3+11x2-6x+5.
5. Hng dn t hc Hot ng ca ThyHot ng ca TrNi dung bi
Thc hin theo quy tcHS lng nghe v ghi vo v BT8
Ta thc hin php nhn sau thu gn ri th tng gi tr vo tnh (c th s dng my tnh b ti)BT9 SGK/8
- GV hi: Gi tr ca biu thc ko ph thuc vo gi tr ca bin khi no ?HS: Khi ta thu gn khng cn bin baBT11 SGK/8
GV: Vy ta phi lm th noHS: Ta thc hin php nhn ri thu gn nu khng cn bin x na th ta chng minh xong
Chun b chu o tit ti luyn tp
IV: RT KINH NGHIM TIT DY :
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Tun:
Ngy son:
Ngy dy:
Lp:
Tit 3
LUYN TP
I MC TIU:- Kin thc: Cng c, khc su kin thc v cc quy tc nhn n thc vi a thc, nhn a thc vi a thc.- K nng: HS thc hin thnh tho php nhn n thc, a thc;bit vn dng linh hot vo tng tnh hung c th.
- Thi : Rn luyn tnh cn thn khi lm ton nhnII. CHUN B:
- Thy: Hnh v sn, phn mu.
- HS: Bi tp v nh, dng hc tp.
III. TIN TRNH TIT DY:
1) n nh: n nh, nm s s HS
2). Kim tra:
Hot ng ca ThyHot ng ca Tr
GV: Gi 2 HS ln bng lm BT 8/8 SGK cu a,b
- Cho HS nhn xt bi lm ca bn.
- Cho HS pht biu hai quy tc (nhn n thc vi a thc, nhn a thc vi a thc)
- GV nhn mnh cc sai lm thng gp ca HS nh du, thc hin xong khng rt gn . . .
- Cui cng GV nhn xt v cho im.HS1:
HS2:
(x2 xy + y2)(x + y) = x3 + x2y x2y xy2 + xy2 + y3 = x3 + y3
3) T chc luyn tp:Hot ng ca ThyHot ng ca TrNi dung bi
+Cho HS gii bi 10
.Gi hai HS ln bng gii cc bi tp 10a) v 10b)
.Cho HS nhn xt
.GV nhn mnh cc sai lm thng gp nh du, thc hin xong khng rt gn...- 2 HS ln bng trnh by.
- HS cn li lm bi vo tp v theo di bn lm nhn xt.
a/ )(x2-2x+3)(1/2x-5)
= 1/2x3-5x2-x2+10x+3/2x-15
= 1/2x3-6x2+x-15
b/ (x2-2xy+y2)(x-y)
= x3-x2y-2x2y+2xy2+xy2-y3= x3-3x2y+3xy2-y3Bi 10/8.
.Thc hin php tnh:
a)(x2-2x+3)(1/2x-5)
=...
=1/2x3-6x2+x-15
b) (x2-2xy+y2)(x-y)
=...
=x3-3x2y+3xy2-y3
+Cho HS gii bi 11
.Hy nu cch gii bi ton: CM gi tr ca biu thc khng ph thuc vo gi tr ca bin?
(Lu HS ta gp lp 7)
.Gi 1 HS ln bng, c lp lm vo v.
Cho HS nhn xt, GV sa sai .
-Nhn mnh: p dng cc quy tc nhn n thc, a thc ri thu gn biu thc, kt qu thu.HS tr li:...
...kt qu sau khi rt gn khng cn cha bin.
.Gi 1 HS ln bng, c lp lm vo v.
(x-5)(2x+3)-2x(x-3) +x+7
= 2x2+3x-10x-15-2x2+6x+x+7
= 8
HS nhn xt bi lm ca bnBi 11/8
Ta c:
(x-5)(2x+3)-2x(x-3) +x+7
=...
=-8
Vy gi tr biu thc cho khng ph thuc vo gi tr ca bin.
Cho HS lm bi 14/8 sgk.
c .
-Hy vit dng tng qut ca 3 s chn lin tip?
(HS thng qun a thuc N, GV b sung).
-Hy vit BTS ch mi quan h tch hai s sau ln hn hai s u l 192 ?
-GV: Tm c a, ta s tm c 3 s cn tm , hy tm a ?
-Gi HS nhn xt bi lm ca bn.
-Vy 3 s cn tm l nhng s no?-HS c .
-HS tr li...
..2a, 2a+2, 2a+4 vi a thuc N
-HS lm bi vo v, 1HS tr li....
(2a+2)(2a+4)- 2a(2a+2)=192
-1HS ln bng, c lp lm bi vo v.
4a2+8a+4a+8-4a2-4a=192
8a = 184
a = 23
-HS nhn xt...
-HS l cc s 46, 48, 50.Bi 14 trang8:
+ Gi 3 s chng lin tip l 2a, 2a + 2, 2a+4 vi a N
Ta c:(2a+2)(2a+4)- 2a(2a+2)=192
.....
a+1=24
a =23
Vy ba s l 46, 48, 50.
Cho HS lm bi 12/8.
-HS lm bi trn phiu hc tp.
-GV thu mt s bi lm trn ca HS chm.
-GVnhn xt, sa sai (nu c).
-Hy nu cc bc gii bi ton Tnh gi tr biu thc khi bit gi tr ca bin?
-HS lm bi trn phiu .
HS:...gm 2 bc:
- Thu gn biu thc
-Thay gi tr ca bin vo BT ri tnhBi 12/8
4. Cng c:Nhn xt tnh hnh hc tp qua tit dy, lu mt s sai lm ca HS thng mt phi.
5. Dn d : Hot ng ca ThyHot ng ca TrNi dung bi
Ta thc hin php nhn sau thu ri ri tm xHS lng nghe v ghi vo vBi tp 13 SGK/9
Ta thc hin php nhn theo quy tcBi tp 15 SGK/9
c trc bi 3 Nhng hng ng thc ng nh sau xem KQ ca bi 15 v NX
IV.RT KINH NGHIM TIT DY:..........................................................................................................................................................................................................................................................................................................................
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Tun:
Ngy son :
Ngy dy:
Lp:Tit 4
3 NHNG HNG NG THC NG NH
I. MC TIU:
- Kin thc: HS nm c cc hng ng thc: bnh phng ca mt tng, bnh phng ca mt hiu, hiu hai bnh phng.
- K nng: Bit vn dng cc hng ng thc trn gii mt s bi tp n gin, vn dng linh hot tnh nhanh nhm.
- Thi : Rn luyn kh nng quan st, nhn xt ng v chnh xc.
II.CHUN B:
Thy: Gio n, SGK, bng ph ghi 3 hng ng thc, bng ph ghi bi, v hnh 1 SGK/9 HS : BTVN. dng hc tp. n li bi c. Xem trc bi mi.III.TIN TRNH TIT DY:
1. n nh: Nm s s lp.2. Kim tra bi c :
Hot ng ca ThyHot ng ca Tr
HS1: -Hy pht biu quy tc nhn hai a thc?
-Gii bi tp 15a).(SGK)
HS1: - Pht biu nh SGK
HS2: -Gii bi tp 15b)
-Tnh (a-b) (a+b) vi a,b l hai s bt k.
HS2:
3. Bi mi:
Gii thiu bi: - Khng thc hin php nhn c th tnh tch trn mt cch nhanh chng hn khng?
Hot ng ca ThyHot ng ca Tr Ni dung bi
Bnh phng cua mot tong.
+HS lm ?1
-Cho HS tnh (a+b) (a+b)
-Rt ra (a+b)2=?
+GV gii thiu tng qut vi A, B l cc biu thc tu :
(A+B)2=A2+2AB+B2.(ghi bng) v gii thiu tn gi Hng ng thc.
-GV dng tranh v sn (H1-SGK),hng dn HS nm c ngha hnh hc ca cng thc.
-HS lm ?2
-Quay li BT 15
.Xc nh dng,cc biu thc A,B.
.i chiu kt qu?
+GV cho HS lm phn p dng.
-Gi HS ng ti ch c kt qu bi a). Yu cu gii thch cch lm.
-Cho HS lm bi b,c trn phiu hc tp.
-GV gi 2 HS ln bng thc hin, kim tra mt s em.
-Cho HS nhn xt, GV sa sai (nu c).
-GV gi 2 HS ln bng thc hin, kim tra mt s em.
-Cho HS nhn xt, GV sa sai (nu c).-HS thc hin:
(a+b)(a+b)=.....
=a2+2ab+b2.
-HS:
(a+b)2=a2+2ab+b2-HS Pht biu bng li:...
-HS: Bi 15a) c dng (A+B)2 vi A=1/2x; B=y.
.HS i chiu kt qu.
-HS tr li:...
.2HS ln bng. HS thc hin trn phiu hc tp.
.HS nhn xt...
.2HS ln bng...
.HS nhn xt...1.Bnh phng ca mt tng:
Vi A,B tu , ta c:
(A+B)2=A2+2AB+B2*.p dng:
a) Tnh:
(a+1)2=... =a2+2a+1
b) x2+4x+4
=... =(x+2)2c) 512=(50+1)2 =502+2.50+1
=2601
3012=(300+1)2
=3002+2.300+1
=90601
Bnh phng cua mot hieu
+Hy vn dng HT trn tnh:
[A+(-B)]2.
*GV lu HS:
[A+(-B)]2 =(A-B)2
-GV gii thiu hng ng thc, cch gi tn .
*GV: ta cng c th tm(A-B)2 bng cch tnh (A-B)(A-B) hy t thc hin theo cch ny v kim tra.
+Cho HS lm ?4.
+Cho HS lm phn p dng.
.Gi 2 HS tnh 2 cu a,b.C lp theo di nhn xt.
.Yu cu HS gii thch cch thc hin cc bi tp trn.
.Gi 1 HS tnh cu c.-HS thc hin:
...=A2-2AB+B2-HS pht biu bng li...
.2HS thc hin trn bng.
.HS nhn xt...
-1HS ln bng, c lp lm vo v, nhn xt.2.Bnh phng ca mt hiu:
Vi A,B tu , ta c:
(A-B)2=A2-2AB+B2+p dng:
a) Tnh:
(x-1/2)2=x2-2.x.1/2+
+(1/2)2=x2-x+1/4
b) (2x-3y)2=
=(2x)2-2.2x.3y+(3y)2 =4x2-12xy+9y2```
Hiu ca hai lp phng:
+Cho HS xem li kt qu bi tp kim tra ming, rt ra:
a2-b2=(a+b)(a-b) .GV gii thiu tng qut vi Av B l cc biu thc tu .
-GV ghi HT ln bng v gii thiu tn gi.
+Cho HS lm ?6.
+Cho HS lm phn p dng.
-Gi 2HS lm cc bi a,b.Yu cu gii thch cch lm, xc nh A,B.
-C lp tnh nhanh cu c) .GV gi HS c kt qu v gii thch cch tnh.
-Cho HS quan st bi ?7 trn bn ph.
Gi HS ng ti ch tr li.
-GV cht li cc HT va hc v cc vn dng ca n vo vic gii bi tp.-HS pht biu bng li...
-HS lm bi v nhp.
.1HS tr li ming.
-HS tr li
.c v Th ng
.Sn rt ra c HT:
(A-B)2=(B-A)23) Hiu ca hai lp phng:
Vi A,B tu , ta c:
A2-B2=(A+B)(A-B)
+p dng:
a) Tnh:
(x+1)(x-1)=x2-1.
(x-2y)(x+2y)
=x2-(2y)2=x2-4y2c) Tnh nhanh:
56.64=(60-4)(60+4)
=602-42 =3600-16
=3584
4. Cng c:
Hot ng ca ThyHot ng ca Tr Ni dung bi
- GV yu cu
* Gi :
1/ c v Th ai ng?
2/ Sn rt ra c HT?
- Cho HS lm cc bi tp Sgk (tr11)
* Gi : xc nh gi tr ca A,B bng cch xem A2 = ? ( A
B2 = ? (B
Yu cu HS nhn xt- HS c ?7 (sgk trang 11)
- Tr li ming:
- Kt lun:
(x y)2 = (y x)2- HS hp tc lm bi theo nhm
- Mi em t trnh by bi lm ca mnh
16b/ 9x2 +y2 +6xy = (3x +y)2
c/ 25a2+4b220ab = (5a-2b)2 - Nhn xt bi lm ca bnBi tp ?7
+ C c v Th u ng
+ HT : (A-B)2 = (B-A)2
Bi Tp 16(bc),
16b/ 9x2 +y2 +6xy = (3x +y)2
c/ 25a2+4b220ab = (5a-2b)2
5. Dn d : -Hc thuc cc hng ng thc 1,2,3
Hot ng ca ThyHot ng ca Tr Ni dung bi
- Hc thuc lng hng ng thc ch du ca hng ng thc
- Bi tp 16 trang 8 Sgk
* p dng HT 1+2- HS nghe dnBi tp 16 trang 11 Sgk
- Bi tp 17 trang 11 Sgk
* VT: p dng HT 1
VP: Nhn n thc vi a thc
(A + B)2 = A2 + 2AB + B2(A-B)2 = A2 2AB+ B2
Bi tp 17 trang 11 Sgk
IV. RT KINH NGHIM TIT DY:..........................................................................................................................................................................................................................................................................................................................
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Tun:
Ngy son :
Ngy dy:
Lp:
Tit 5
LUYN TPI. MC TIU:
- Kin thc: Cng c kin thc v cc hng ng thc : Bnh phng ca mt tng , bnh phng ca mt hiu , hiu hai bnh phng.
- K nng: HS vn dng thnh tho cc hng ng thc trn vo gii ton.
- Thi : Pht trin t duy logic , thao tc phn tch , tng hp.
II.CHUN B:
Thy: Gio n. Phiu HT. Bng ph.
HS : n bi c + lm BTVN.
III.TIN TRNH TIT DY:
1)n nh2) Kim tra:
Hot ng ca ThyHot ng ca Tr Ni dung bi
- Treo bng ph kim tra
- Kim v bi lm nh (3HS)
- Cho HS nhn xt
- GV nh gi cho im - Mt HS ln bng, cn li chp vo v v lm bi ti ch.
a) (x+1)2
b) (5a-2b)2
- Nhn xt bi lm bng
- T sa sai (nu c) 1/ Vit ba HT hc (6)
2/ Vit cc bthc sau di dng bnh phng 1 tng (hiu) (4)
a. x2 +2x +1
b. 25a2 +4b2 20ab
3) Luyen tap:
Hot ng ca ThyHot ng ca Tr Ni dung bi
+Cho HS gii bi tp 16
-Gi 2 HS ln bng
-C lp theo di ,nhn xt
-GV nhn xt , sa sai (nu c)-HS1 gii bi a
-HS1gii bi d 1) Bi 16/11
a/ x2 +2x +1 = (x+1)2
d/ x2 x +1/4
=x2 2.x.1/2 + (1/2)2
=(x-1/2)2
+ Cho HS lm bi 18
-Gi 1 HS ln bng
-GV gip 1 s HS yu nhn dng hng ng thc mi bi , xc nh A v B tm c hng t phi tm
-Gi HS nu bi tng t , 1 HS khc in vo ch trng .
- GV m rng : cho cc bi.
a) ...-12xy +... = (3x- ...)2
b) .... + 3x + ....= (x+...)2
c) ... +8xy + ... = (...+...)2
. Gi HS ng ti ch tr li , GV ghi bng.
. cu c ta cn cch in no khc.-1HS ln bng
- C lp theo di nhn xt
-1HS cho , HS khc in vo ch trng
- HS tr li
HS :
c1)x2 + 8xy + 16y2=(x+4y)2 c2)4x2+8xy+4y2 =(2x+2y)22)Bi 18: Khi phc cc hng ng thc:
a) x2+6xy+...=(...+3y)2x2+6xy+9y2 =(x+3y)2
b) ...-10xy +25y2 = (...-...)2x2-10xy+25y2=(x-y)2
Bi tp thm :
Kt qu:
a)9x2-2xy+4y2=(3x-2y)2
b)x2+3x+9/4 =(x+3/2)2
+Cho HS gii bi 17
-GV ghi : CM rng :
(10a+5)2= 100a . (a+1)+25
-Hy nu cch chng minh (GV ghi bng , sa sai nu c)
-Vn dng kt qu trn tnh:
252 =? 352 =?
652 =? 852 =?
HS tr li
HS tr li nhanh
252 = 625
352 = 1225
652 = 4225
852 = 7225
3)Bi 17 :
Ta c :
100a.(a+1) +25
=100a2+100a+25
=(10a)2 +2.10a.5 +52
=(10a+5)2
+Cho HS gii bi 20
. GV ghi ng thc :
x2+2xy+4y2 =(x+2y)2. Kt qu trn l ng hay sai , gii thch
. GV lu HS : y l trng hp nhm ln m HS thng mc phi
+Cho HS gii bi 23
. GV ghi : c/minh rng :
(a+b)2 = (a-b)2 +4ab
(a-b)2= (a+b)2- 4ab
. Cho HS lm theo nhm
. Gi 2 i din ln bng gii , GV kim tra 1 s nhm
. Cho HS nhn xt , GV nh gi , sa sai(nu c)
. c/minh A=B c nhng cch no ?
-Gi HS tnh phn p dng , GV ghi bng
-Vi bi tp trn ta thy nu bit tng (hiu) v tch ta s tm c hiu (tng) ca 2 s ta s tm c 2 s cho
-Cc cng thc c c/minh trn cho ta mi lin h gia bnh phng ca 1 tng v bnh phng ca 1 hiu , sau ny cn c ng dng trong vic tnh ton , c/minh ng thc.
.Cho HS lm nhanh bi 22 trn phiu hc tp
HS suy ngh tr li
.HS hot ng nhm
. 2 i din ln bng thc hin
. HS nhn xt
. HS tr li ming
C1: Nu c 1 v phc tp , ta thu gn v phc tp
_ kt qu thu gn chnh l v n gin.
C2: Nu c
A-B=C th A=B
C3: Nu c
A=C
C=B
th A=B
.HS lm bi trn phiu hc tp
4) Bi 20 :
Cch vit :
x2+2xy+4y2=(x+2y)2l sai
V :
(x+2y)2=x2+2x2y +2y)2=x2+4xy+4y25) Bi 23:
a)Ta c :
(a-b)2+4ab
=a2-2ab+b2+4ab
=a2+2ab+b2= (a+b)2Vy(a+b)2=
(a-b)2+4ab
b)
(a+b)2 - 4ab
=a2+2ab+b2- 4ab
=.....
= (a-b)2Vy(a-b)2=
(a+b)2- 4ab
p dng
a)Vi a+b=7, a.b=12
th (a-b)2=72-4.12=1
b)Vi a-b=20,a.b=3
th (a+b)2=202+4.3=412
. GV thu , chm nhanh 1 s HS.. Kt qu:
a)1012=(100+1)2 =...=10201
b)1992=(200-1)2 =...=39601
c)47.53=(503)(50+3)
=...=2491
4. Cng c:Nu nhn xt u khuyt im ca HS qua gi luyn tp5. Dn d:
Hot ng ca ThyHot ng ca Tr Ni dung bi
- Xem li li gii cc bi gii.
- Bi tp 22 trang 11 Sgk
* Tch thnh bnh phng ca mt tng hoc hiu
- Bi tp 24 trang 11 Sgk* Dng HT
- Bi tp 25 trang 11 Sgk
* Tng t bi 24(A + B)2 = A2 + 2AB + B2(A-B)2 = A2 2AB+ B2
- HS nghe dn v ghi ch vo v
Bi tp 22 trang 12 Sgk
Bi tp 24 trang 12 Sgk
Bi tp 25 trang 12 Sgk
IV. RT KINH NGHIM TIT DY:..........................................................................................................................................................................................................................................................................................................................
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Tun:
Ngy son :
Ngy dy:
Lp:
Tit 6
4 NHNG HNG NG THC NG NH (tt)
I. MC TIU:
- Kin thc: Nm c cc hng ng thc : Lp phng ca mt tng , lp phng ca mt hiu.
- K nng: Bit vn dng cc hng ng thc trn gii bi tp
- Thi : Rn luyn k nng tnh ton , cn thn.
II.CHUN B:
Thy: Gio n. Phn mu
HS : Gii bi tp v nh. + Hc thuc cc hng ng thc
(A+B)2 , (A-B)2 , A2 B2III.TIN TRNH TIT DY:
1) n nh: 2) Kim tra bi c:
Hot ng ca thyHot ng ca trNi dung bi
- Treo bi
- Gi mt HS ln bng
- Cho HS nhn xt bng
- nh gi cho im - Mt HS ln bng
- HS cn li lm vo v bi tp
1/ = 9x2 6xy + y2
2/ = 4x2 1/ Vit 3 hng ng thc (6)
2/ Tnh :
a) (3x y)2 = (2)
b) (2x + )(2x - ) (2)
3) Bi mi:
GV vo bi trc tip: ta hc ba hng ng thc bc hai Chng ta tip tc nghin cu v cc hng ng thc bc baHot ng ca thyHot ng ca trNi dung bi
Lp phng ca 1 tng :
GV : Ta c th rt gn (a+b)(a+b)2 = (a+b)3(a+b)3 = a3+3a2b+3ab3+b3
Vi a,b l cc s tu , ng thc trn lun ng
-Ta c y l mt hng ng thc ng nh na , GV gii thiu bi mi- GV gii thiu tng qut vi A v B l cc biu thc tu ta cng c
(A+B)3 = A3+3A2B+3AB2+B3. GV gii thiu cch gi tn hng ng thc v ghi bng.
. Hy pht biu hng ng thc trn bng li
-Cho HS thc hin phn p dng
. HS lm bi vo v
. Gi 2 HS ln bng tnh . Yu cu HS trnh by cch lm sau khi gii , xc nh r A,B trong cch p dng
. GV nhn xt , sa sai (nu c)- HS pht biu bng li
- HS lm bi vo v
- 2 HS ln bng
a) A=x , B =1
b) A=2x , B =y4)Lp phng ca 1 tng :
Vi A, B tu ta c:
(A+B)3 = A3+3A2B+3AB3+B3 (4)
*p dng :
a) Tnh :
(x+1)3 = =x3+3x21+3x.13+13=x3+3x2+3x+1
b)Tnh :
(2x+y)3
= (2x)3+3.(2x)2y + 3.2x.y2+y3=8x3+12x2y+6xy2+y3
Lp phng ca mt hiu:
- Cho HS lm bi 23
Tnh [a+(-b)]3 (vi a,b l cc s tu )
. HS lm trn phiu hc tp
. Gi 1 HS ln bng thc hin , GV kim tra 1 s HS.
. Cho HS nhn xt
. Ta c : a+(-b) = a-b
(a-b)3 = ?
. GV gii thiu tng qut vi A,B tu v cch gi tn hng ng thc .
- Hy pht biu hng ng thc (5) bng li.
- Cho HS lm phn p dng
. C lp cng lm bi a,b : gi 2HS ln bng gii , yu cu trnh by cch gii , xc nh A,B.
. GV lu HS thng xc nh B sai
VD: a) B= -1/3
b) B= -2y
. HS lm trn phiu hc tp
. HS i chiu vi bi lm ca mnh v cho nhn xt.
. HS tr li ...
. HS pht biu bng li
. C lp cng lm
. 2 HS ln bng gii
a) A=x , B= 1/3
b) A=x , B= 2y5)Lp phng ca mt hiu:
Vi A,B tu , ta c
(A-B)3
= A3-3A2B+3AB2-B3 (5)
*p dng :
a)Tnh:
(x-1/3)3=x3-3.x2.1/3 +3.x.(1/3)2+(1/3)3= x3-x2+x/3+1/27
b)Tnh:
(x-2y)3=x3-3.x2.2y3 +3.x.(2y)2+(2y)3=x3-6x2y+12xy2+8y3
. HS thc hin cu c trn phiu hc tp ca nhm .
. GV kim tra kt qu ca cc nhm
. Chn 1 i din nhm trnh by bi gii ca nhm .
. Cho HS nhn xt.- HS thc hin theo nhm trn phiu h tp.
.1 i din nhm trnh by bi gii
. Cc nhm so snh kt qu ,nhn xt
Kq :
1),3) ng
2),4),5) Sai
Nhn xt:
(A-B)2 = (B-A)2(A-B)3 = -(B-A)3
4. Cng c:
Hot ng ca thyHot ng ca trNi dung bi
. Cho HS nhc li cc HT hc
. GV lu HS v s x du trong HT (a-b)3; khc su cho HS : du m ng trc lu tha bc l ca b. HS tr li.
5. Dn dHot ng ca thyHot ng ca trNi dung bi
- Hc bi: vit cng thc bng cc ch tu , ri pht biu bng li.
- Bi tp 26 trang 12 Sgk
* p dng hng ng thc 4,5
- Bi tp 27 trang 12 Sgk
* Tng t bi 26
- Bi tp 28 trang 12 Sgk* Tng t bi 26- HS nghe dn v ghi ch vo v
(A+B)3= A3+3A2B+3AB2+B3(A-B)3= A3-3A2B+3AB2 -B3Bi tp 26 trang 12 Sgk
Bi tp 27 trang 12 Sgk
Bi tp 28 trang 12 Sgk
IV. RT KINH NGHIM TIT DY:..........................................................................................................................................................................................................................................................................................................................
Tun:
Ngy son :
Ngy dy:
Lp:
Tit 7
5. NHNG HNG NG THC NG NH (tt)
I.MC TIU:
- Kin thc: HS nm c cc hng ng thc: Tng hai Lp phng, hiu hai lp phng.
- K nng: Bit vn dng cc hng ng thc mt cch linh hot gii bi tp.- Thi : Rn luyn tnh cn thn trong lm ton.
II. CHUN B:
Thy: Bng ph ghi bi tp, phn mu
HS: Hc thuc bi c + gii bi tp v nh
III. TIN TRNH TIT DY:
1. n nh 2. Kim tra bi c :
Hot ng ca thyHot ng ca trNi dung bi
- Treo bi
- Gi mt HS ln bng
- Cho HS nhn xt bng
- nh gi cho im - Mt HS ln bng
- HS cn li lm vo v bi tp
1/ = 9x2 6xy + y2
2/ = 4x2 1/ Vit 3 hng ng thc (6)
2/ Tnh :
a) (3x y)2 = (2)
b) (2x + )(2x - ) (2)
3. Bi mi: GV vo bi trc tip: ta hc ba hng ng thc bc hai Chng ta tip tc nghin cu v cc hng ng thc bc ba
Hot ng ca thyHot ng ca trNi dung bi
- Nu ?1 , yu cu HS thc hin
- T ta rt ra a3 + b3 = ?
- Vi A v B l cc biu thc tu ta c?
- Yu cu HS pht biu bng li hng ng thc
- GV pht biu cht li: Tng hai lp phng ca hai bthc bng tch ca tng hai bthc vi bnh phng thiu ca hiu hai bthc o.
- Ghi bng bi ton p dng
- GV gi HS nhn xt v hon chnh - HS thc hin ?1 cho bit kt qu:
(a + b)(a2 ab + b2) = = a3 + b3
A3+B3= (A+B)(A2-AB+B2)
- HS pht biu bng li
- HS nghe v nhc li (vi ln)
- Hai HS ln bng lm
a) x3+8 = (x+8)(x2- 2x+ 4)
b) (x+1)(x2 x+1) = x3 + 16. Tng hai lp phng:Vi A v B l cc biu thc tu ta c:
A3+B3= (A+B)(A2-AB+B2)
Qui c gi A2 AB + B2 l bnh phng thiu ca mt hiu A B
Ap dng:
a) x3+8 = (x+8)(x2- 2x+ 4)
b) (x+1)(x2 x+1) = x3 + 1
- Nu ?3 , yu cu HS thc hin
- T ta rt ra a3 - b3 = ?
- Vi A v B l cc biu thc tu ta c?
- Ni v ghi bng qui c, yu cu - HS pht biu bng li Ht
- GV pht biu cht li: Hiu hai lp phng ca hai bthc bng tch ca hiu hai bthc vi bnh phng thiu ca tmg hai bthc o.
- Treo bng ph (bi ton p dng), gi 3HS ln bng .
- Cho HS so snh hai cng thc va hc
- GV cht li vn -HS thc hin ?3 cho bit kt qu:
(a -b)(a2 + ab + b2) = = a3 - b3
A3-B3= (A-B)(A2+AB+B2)
- HS pht biu bng li
- HS nghe v nhc li (vi ln)
- Ba HS lm bng (mi em mt bi), cn li lm vo v
a) (x 1)(x2+x+1) = x3 1
b) 8x3 y3 = (2x)3 y3
= (2x y)(4x+2xy+y2)
c) (x +2)(x2 -2x + 4) = x3 - 23
= x3 8
- Nhn xt bng sau khi lm xong
- HS suy ngh, tr li
- HS theo di v ghi nh 7. Hiu hai lp phng:
Vi A v B l cc biu thc tu ta c:
A3-B3= (A-B)(A2+AB+B2)
Qui c gi A2 + AB + B2 l bnh phng thiu ca mt tng A + B
Ap dng:
a) (x 1)(x2+x+1) = x3 1
b) 8x3 y3 = (2x)3 y3
= (2x y)(4x+2xy+y2)
c) (x +2)(x2 -2x + 4) = x3 - 23
= x3 8
A3+B3 = (A+B)(A2-AB+B2)
A3-B3 = (A -B)(A2+AB+B2)
4. Cng c:
Hot ng ca thyHot ng ca trNi dung bi
- Gi HS ln lt nhc li by hng ng thc hc (treo bng ph v m ra ln lt)
- Khi A = x, B = 1 th cc cng thc trn c vit di dng nh th no?
- GV cht li v ghi bng - HS thay nhau nu cc hng ng thc hc
(A+B)2 = A2 + 2A + B2(A B)2 =A2 2A + B2 A2 B2= (A +B)(A -B)
(A +B)3=A3+3A2 B+3AB2+B3
(A -B)3 = A3 3A2B+3AB2 B3
A3 + B3 =(A +B)(A2 -AB +B2)
A3 B3 =(A B)(A2+AB+B2)- Ta c by hng ng thc ng nh:
(A+B)2 = A2 + 2A + B2(A B)2 =A2 2A + B2 A2 B2= (A +B)(A -B)
(A +B)3=A3+3A2 B+3AB2+B3
(A -B)3 = A3 3A2B+3AB2 B3
A3 + B3 =(A +B)(A2 -AB +B2)
A3 B3 =(A B)(A2+AB+B2)
5. Dn d:Hot ng ca thyHot ng ca trNi dung bi
- Vit mi cng thc nhiu ln.
- Din t cc hng ng thc o bng li.
- Bi tp 30 trang 16 Sgk
* p dng hng ng thc 6,7
- Bi tp 31 trang 16 Sgk
* Tng t bi 30
- Bi tp 32 trang 16 Sgk* Tng t bi 30- HS nghe dn
x3 + 1 = (x +1)(x2 - x +1)
x3 1 = (x 1)(x2 + x + 1)
- Ghi ch vo v Bi tp 30 trang 16 Sgk
Bi tp 31 trang 16 Sgk
Bi tp 32 trang 16 Sgk
IV. RT KINH NGHIM TIT DY:.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Tun:
Ngy son :
Ngy dy:
Lp:
Tit 8
LUYN TP (5)I. MC TIU:
- Kin thc: Cng c kin thc v 7 hng ng thc ng nh.
- K nng: HS bit vn dng kh thnh tho cc hng ng thc ng nh vo bi ton.
- Thi : Hng dn HS cch dng hng ng thc (A ( B)2 xt gi tr ca mt s tam thc bc hai.
II. CHUN B:
Thy: Bng ph ghi bi tp, phn mu
HS: - Hc thuc lng 7 HT ng nh
- Bng nhm
III. TIN TRNH TIT DY:
1. n nh
2. Kim tra bi c :
Hot ng ca thyHot ng ca trNi dung bi
- Treo bng ph a ra kim tra. Gi mt HS
- Thu v kim giy vi em
- Cho HS nhn xt
- Sa sai v nh gi cho im - Mt HS ln bng, cn li lm vo giy
a) 8x3 1=(2x-1)(4x2+2x+1)
b)27+64y3=(3+4y)(9-24y+16y2)
- HS c gi np giy lm bi.
- Nhn xt bi lm bng
- T sa sai (nu c). 1/ Vit cng thc tng hai lp phng, hiu hai lp phng (5)
2/ Vit cc biu thc sau di dng tch: (5)
a) 8x3 1
b) 27 + 64y3
3. Luyen tap :Hot ng ca thyHot ng ca trNi dung bi
- Ghi bi tp 31 ln bng , cho mt HS ln bng trnh by li gii, GV kim v bi lm HS
- Cho HS nhn xt li gii ca bn, sa cha sai st v cht li vn (v cch gii mt bi chng minh ng thc). - HS ln bng trnh by li gii, cn li trnh v bi lm trc mt
- HS nhn xt sa sai bi lm bng
- HS nghe ghi hiu hng gii bi ton cm ng thc Bi 31 trang 16 Sgk
a)VP: (a + b)3 3ab(a + b)
= a3 + 3a2b+ 3ab2+ b33a2b 3ab2 = a3 + b3 .
Vy :a3 + b3 = (a+b)3-3ab(a+b)
b) (a b)3 + 3ab(a-b) = a3 3a2b +3ab2 b2 = a3- b3
-Treo bng ph.Gi mt HS ln bng, yu cu c lp cng lm
- Cho vi HS trnh by kt qu, c lp nhn xt
- GV nhn xt v hon chnh- HS lm vic c nhn
- Mt HS lm bng
a) (2+xy)2 = 4 + 4xy + x2y2
b) (5 -3x)2 = 25 - 30x + 9x2
c) (5 x2)(5+ x2) = 25 x4
d) (5x 1)3=125x350x2+15x1
e)(x -2y)(x2 +2xy + 4y2)=x3- 8y3
f) (x+3)(x2-3x+9) = x3 + 27
- Trnh by kt qu c lp nhn xt, sa sai (nu c)
- T sa sai v ghi vo v Bi 33 trang 16 Sgk
a) (2+xy)2 = 4 + 4xy + x2y2
b) (5 -3x)2 = 25 - 30x + 9x2
c) (5 x2)(5+ x2) = 25 x4
d) (5x 1)3= 125x3 50x2 + 15x 1
e) (x -2y)(x2 +2xy + 4y2)=x3- 8y3
f) (x+3)(x2-3x+9) = x3 + 27
- Ghi bi 34 ln bng, cho HS lm vic theo nhm nh t pht
- Gi i din mt vi nhm nu kt qu, cch lm
- GV ghi bng kim tra kt qu - HS lm bi tp theo nhm nh cng bn
- i din nu cch lm v cho bit p s ca tng cu
- Sa sai vo bi (nu c) Bi 34 trang 17 Sgk
a) (a+b)2 (a-b)2 = = 4ab
b) (a+b)3-(a-b)3-2b3 == 6a2b
c) (x+y+z)22(x+y+z)(x+y)+(x+y)2
= = z2
- Ghi bng bi 35 ln bng
- Hi: Nhn xt xem cc php tnh ny c c im g? (cu a? cu b?)
- Hy cho bit p s ca cc php tnh. GV trnh by li - HS ghi bi vo v
- HS suy ngh tr li
a) C dng bnh phng ca mt tng
b) Bnh phng ca mt hiu
- HS lm vic c th-nu kt qu Bi 35 trang 17 Sgk
a) 342 + 662 + 68.66
= 342 + 662 + 2.34.66 = (34 + 66)2
= 1002 = 10.000
b)742 + 242 48.74
= 742 + 242 2.24.74
= (74 24)2 = 502 = 2500.
4. Cng c:
Hot ng ca thyHot ng ca trNi dung bi
- Chia 4 nhm hot ng, thi gian (3).
- GV quan st nhc nh HS no khng tp trung
- Sau gi i din nhm trnh by
- Yu cu cc nhm nhn xt ln nhau - HS chia nhm lm bi
- Cu 1 b ng
- Cu 2 d ng
- Cu 3 b ng
-C i din nhn xt bi ca nhm khc1/ Rt gn (x+1)3-(x-1)3 ta c:
a) 2x2+2 b)2x3+6x2
c) 4x2+2 d)Kt qu khc
2/Phn tch 4x4+8x2+4 thnh tch
a)(4x+1)2 b) (x+2)2c)(2x+1)2 d) (2x+2)23/ Xt (2x2 +3y)3=4x3 + ax4y + 18x2y2 +by3. Hi a,b bng ?
a/ a=27 b=9 b)a=18 b=27
c/ a=48 b=27 d)a=36 b=27
5. Dn d:
- Hc li cc hng ng thc
- Bi tp 36 trang 17 Sgk
* Bin i sau thay gi tr
- Bi tp 38 trang 17 Sgk* Phan tch tng v sau sosnh- Xem li tnh cht php nhn phn phi i vi php cng- HS nghe dn , ghi ch vo v
- p dng hng ng thc 1,4
- p dng 7 hng ng thcBi tp 36 trang 17 Sgk
Bi tp 38 trang 17 Sgk
IV. RT KINH NGHIM TIT DY:.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
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Ngy son :
Ngy dy:
Lp:
Tit 9
6. PHN TCH A THC THNH NHN T BNG
PHNG PHP T NHN T CHUNGI. MC TIU:
- Kin thc: HS hiu th no l phn tch a thc thnh nhn t.
- K nng: Bit cch tm nhn t chung v t nhn t chung
- Thi : Rn luyn tnh cn thn trong lm ton.
II. CHUN B:
Thy: Bng ph, ghi bi tp
Tr: Bng nhm
III. TIN TRNH TIT DY:
1. n nh
2. Kim tra bi c : Hot ng ca thyHot ng ca trNi dung bi
- Treo bng ph. Gi mt HS ln bng. C lp cng lm bi tp
- Kim tra bai tp v nh ca HS
- Cho HS nhn xt bng
- GV nh gi cho im - Mt HS ln bng vit cng thc v lm bi
- C lp lm vo v bi tp
Nhn xt, nh gi bi lm ca bn trn bng
(a+b)2 +(a b)2 = = 2a2 + 2b2 - Vit 7 ht ng nh: (7)
(x+y)2 =
(x -y)2 =
x2 y2 =
(x+y)3 =
(x y)3 =
x3 +y3 =
x3 y3 =
- Rt gn biu thc: (3)
(a+b)2 + (a b)2 =
3. Bi mi :
V: Chung ta a biet phep nhan a thc v du: (x +1)(y - 1)=xyx+y 1 thc chat la ta a bien oi ve trai thanh ve phai. Ngc lai, co the bien oi ve phai thanh ve trai?
Hot ng ca thyHot ng ca trNi dung bi
- Nu v ghi bng v d 1
- n thc 2x2 v 4x c h s v bin no ging nhau ?
- GV cht li v ghi bng
Ni:Vic bin i nh trn gi l phn tch a thc thnh nhn t.
- Vy phn tch a thc thnh nhn t l g?
- Cch lm nh trn gi l phng php t nhn t chung
- Nu v d 2, hi: a thc ny c my hng t? Nhn t chung l g?
- Hy phn tch thnh nhn t?
- GV cht li v ghi bng bi gii
- Nu ch ly 5 lm nhn t chung ? 2x2 = 2x . x
4x = 2x . 2
- HS ghi bi vo tp
- Phn tch a thc thnh nhn t l bin i a thc thnh mt tch ca nhng a thc
- HS hiu th no l phng php t nhn t chung
- HS suy ngh tr li:
+ C ba hng t l
+ Nhn t chung l 5x
- HS phn tch ti ch
- HS ghi bi
- Cha n kt qu cui cng 1/ V d 1:
Hy phn tch a thc 2x2 4x thnh tch ca nhng a thc.
2x2-4x = 2x.x+2x.2 = 2x(x-2)
V d 2:
Phn tch a thc sau thnh nhn t 15x3 - 5x2 +10x
Gii: 15x3 - 5x2 +10x =
= 5x.3x2 - 5x.x + 5x.2
= 5x.(3x2 x +2)
- Ghi ni dung ?1 ln bng
- Yu cu HS lm bi theo nhm nh, thi gian lm bi l 5
- Yu cau i din nhm trnh by
- Cc nhm nhn xt ln nhau
- GV sa ch sai v lu cch i du hng t c nhn t chung
- Ghi bng ni dung ?2
* Gi : Mun tm x, hy phn tch a thc 3x2 6x thnh nhn t
- Cho c lp nhn xt v cht li - HS lm ?1 theo nhm nh cng bn.
- i din nhm lm trn bng ph. Sau trnh by ln bng
a) x2 x = x.x x.1 = x(x-1)
b) 5x2(x 2y) 15x(x 2y)
= 5x.x(x-2y) 5x.3(x-2y)
= 5x(x-2y)(x-3)
c) 3(x - y) 5x(y - x)
= 3(x - y) + 5x(x - y)
= (x - y)(3 + 5x)
- C lp nhn xt, gp
- HS theo di v ghi nh cch i du hng t
- Ghi vo v bi ?2
- Nghe gi , thc hin php tnh v tr li
- Mt HS trnh by bng
3x2 6x = 0
( 3x . (x 2) = 0
( 3x = 0 hoc x 2 = 0
( x = 0 hoc x = 2
- C lp nhn xt, t sa sai 2/ Ap dng :
Gii?1 :
a) x2 x = x.x x.1 = x(x-1)
b) 5x2(x 2y) 15x(x 2y)
= 5x.x(x-2y) 5x.3(x-2y)
= 5x(x-2y)(x-3)
c) 3(x - y) 5x(y - x)
= 3(x - y) + 5x(x - y)
= (x - y)(3 + 5x)
* Ch : A = - (- A)
Gii ?2 :
3x2 6x = 0
( 3x.(x 2) = 0
( 3x = 0 hoc x 2 = 0
( x = 0 hoc x = 2
4. Cng c:
Hot ng ca thyHot ng ca trNi dung bi
- Cho HS lm bi 39/19 SGK
( GV chia lp thnh 2, mt na gii cu b, d, mt na gii cu c, e
( GV nhc nh HS cch tm cc s hng vit trong ngoc: ly ln lt cc hng t chia cho nhn t chung.
( GV nhn xt bi lm ca HS
- Cho HS lm bi 40b/19
( tnh nhanh gi tr ca biu thc ta nn lm th no?
- HS lm bi trn bng nhm
kt qu:
b) x2 (+ 5x + y)
c) 7xy(2x 3y + 4xy)
d) (y 1) (x y)
e) 2( x y) (5x + 4y)
( HS nhn xt bi lm ca bn
( Yu cu HS lm vo v, 1 HS ln bng gii - HS nn phn tch a thc thnh nhn t ri mi thay gi tr ca x v y vo tnh
- HS lm vo v, 1 HS ln bng Bi 40b
Ta c:
x(x 1) y(1 x)
= x(x - 1) + y(x 1)
= (x 1) (x + y)
Thay x = 1999 vo biu thc ta c:
(2001 1) (2001 + 1999)
= 2000 . 4000
= 8000000
5. Dn d:Hot ng ca thyHot ng ca trNi dung bi
- c Sgk lm li cc bi tp v xem li cc bi tp lm
- Bi 41 trang 19 Sgk
* Tng t ?2
- Bi 42 trang 19 Sgk
* 55n+1 = ?
- Xem li 7 hng ng thc tit sau hc bi 7- HS nghe dn v ghi ch vo tp
- Ch du, t n kt qu cui cng
- Nhn 2 lu tha cng c s
- Xem li 7 hng ng thc ng nh Bi 41 trang 19 Sgk
Bi 42 trang 19 Sgk
IV. RT KINH NGHIM TIT DY:.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
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Ngy son :
Ngy dy:
Lp:
Tit 10
7. PHN TCH A THC THNH NHN T BNG
PHNG PHP DNG HNG NG THC
I. MC TIU1. Kin thc : HS hiu cch phn tch a thc thnh nhn t bng phng php dng hng ng thc.
2. K nng : HS bit vn dng cc hng ng thc hc vo vic phn tch a thc thnh nhn t. Vn dng gii ton.
3. Thi : Rn k nng quan st, linh hot khi lm ton. II. CHUN B:- Thy:+ Bng ph ghi cc bi tp mu
+ kim tra 15pht
- HS: Bng nhm + n bi c.
III. TIN TRNH TIT DY:1. n nh 2. Kim tra: Cho HS kim tra 15 pht .Cu hip n
Cu 1: Vit tip vo v phi c cc hng ng thc :
A2 + 2AB + B2 =
A2 ( 2AB + B2 =
A2 B2 =
A3 + 3A2B + 3AB2 + B3 = A3 ( 3A2B + 3AB2 ( B3 = A3 + B3 =
A3 ( B3 =
Cu 2: Tm x bit :
x3 13x = 0
1. A2 + 2AB + B2 = (A + B)2A2 ( 2AB + B2 = (A ( B)2A2 B2 = (A + B)(A B)A3 + 3A2B + 3AB2 + B3 = (A + B)3
A3 ( 3A2B + 3AB2 ( B3 = (A B)3A3 + B3 = (A + B)(A2 AB + B2)A3 ( B3 = (A ( B)(A2 ( AB + B2)
2. Tm x bit :x3 13x = 0
x(x 13) = 0
x = 0 hoc x 13 = 0
x = 0 hoc x = 13
3. Bi mi:Hot ng ca thyHot ng ca trNi dung bi
Cho HS thc hin phn v d:
GV ghi ln bng 1. V d
Phn tch cc a thc sau thnh nhn t
( Xt v d a): c th dng phng php t nhn t chung phn tch a thc x2 4x + 4 thnh nhn t c khng? V sao
( GV: a thc ny c 3 hng t, em hy ngh xem c th p dng HT no bin i thnh tch?HS: Khng thc hin c v tt c cc hng t ca a thc khng c nhn t chung.
HS: a thc trn c th vit c di dng (A B)2a) x2 4x + 1
b) x2 2
c) 1 8x3gii
a) x2 4x + 4
= x2 2x .2 + 22= (x 2)2b) x2 2 = x2 ()2= (x + ) (x - )
c) 1 8x3 = 1 (2x)3= (1 2x) (1 + 2x + 4x2)
( GV gi HS thc hin
( GV gii thiu cch lm nh trn gi l phn tch a thc thnh nhn t bng phng php HT( HS tr li ming (gv ghi bng)
( GV yu cu HS t nghin cu hai v d b v c trong sch gio khoa trang 19
( Qua phn t nghin cu em hy cho bit mi v d s dng HT no phn tch a thc thnh nhn t?
- GV hng dn HS lm
a) Phn tch a thc
x3 + 3x2 + 3x + 1 thnh nhn t: ( HS t nghin cu SGK, 2HS ln trnh by
( HS tr li:
A2 B2, v d c dng HT: A3 B3
- a thc ny c 4 hng t, bc cao nht ca bin l 3, theo em c th p dng hng ng thc no?HS: C th dng HT (A + B)3
( Gi HS thc hin( Mt HS thc hin
x3 + 3x2 + 3x + 1
= x3 + 3.x2.1 + 3x.12 + 13= (x + 1)3
b) Phn tch a thc
(x + y)2 - 9x2 thnh nhn t
( Gi HS nhn dng biu thc
( Gi HS thc hin
( Gi HS nhn xt( HS: a thc c dng A2 B2( HS thc hin
(x + y)2 9y2= (x + y)2 (3y)2= (x + y + 3x) (x + y 3x)
= (4x + y) (y 2x)
- Yu cu HS thc hin tip
( Gi HS nhn xt
- 1 HS ln bng, c lp lm v nhp
1052 25 = 1052 - 52= (105 5) (105 + 5)
= 100 . 110
= 11000
- Cho HS lm phn p dng
( GV cho HS quan st bi trn bng ph( HS c bi2. p dng
( chng minh a thc chi ht cho 4 vi mi s nguyn n cn lm th no.( HS .bin i a thc thnh dng tch trong c c 1 tha s l bin ca HV d: (SGK trg 26)
gii:
Ta c:
(2n + 5)2 25
= (2n + 5)2 - 52= (2n + 5-)(2n+5+5)
= 2n (2n + 10)= 4n (n + 5)
( y thc t l i phn tch a thc thnh nhn tNn (2n + 5)2 25 chia ht cho 4 vi mi s nguyn n
( Cho HS lm bi vo v, 1 HS ln bng lm- HS lm vo v, 1HS ln bng lm, HS lm bi vo v
( Cho HS nhn xt, GV sa sai (nu c).- HS nhn xt bi lm ca bn
4. Cng c:
Hot ng ca thyHot ng ca trNi dung bi
Cho HS lm bi tp 43/20 SGK
( Cho mi dy lm 2 bi (a v c, b v d)( HS lm vo v theo quy nh ca GV
( Gi 4 HS ln bng gii( 4 HS ln bng gii
( GV nhn xt, sa sai nu c( HS nhn xt bi gii kt qu:
a) (x + 3)2 b) (x + 5)2c) (2x-)(4x2 + x +)
d) (x 8y)(x + 8y)
5. Dn d:
- n li bi, ch vn dng hng ng thc cho ph hp
- Gii cc bi tp 44, 45, 46/20 SGK + 29, 30/6 SGK
IV. RT KINH NGHIM TIET DY:..........................................................................................................................................................................................................................................................................................................................
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Tun:
Ngy son :
Ngy dy:
Lp:
Tit 11
8. PHN TCH A THC THNH NHN T BNG PHNG PHP NHM HNG T
I. MC TIU:
1. Kin thc :HS bit phn tch a thc thnh nhn t bng phng php nhm hng t .
2. K nng : HS bit nhm cc hng t mt cch thch hp phn tch a thc thnh nhn t, khi nhm cc hng t ng trc du ngoc l du th i du cc hng t trong du ngoc, vn dng phn tch a thc thnh nhn t mt s dng ton .
3. Thi : Rn k nng quan st, linh hot khi gii ton.II. CHUN B:
Thy: Bng ph ghi bi gii mu, bi.
Tr: Bng nhm
III. TIN TRNH TIT DY:
1. n nh 2. Kim tra Gi 2 HS ln bng
HS1: Cha bi 44c/20 SGK
(a + b)3 + (a b)3
= (a3 + 3a2b + 3ab2 + b3) + (a3 - 3a2b + 3ab2 - b3)
= 2a3 + 6ab2= 2a(a2 + 3b2)
Hi thm: cn cch gii no khc khng?
HS: Dng hng ng thc A3 + B3GV: Cho hc sinh quan st bi gii theo cch trn (ghi sn bng ph)
(a + b)3 + (a - b)3= [(a + b) + (a b)][(a + b)2 (a + b)(a-b)+(a-b)2]
= (a + b + a b)(a + 2ab + b2a2 +b2 +a2 2ab+b2)
= 2a(a3 + 3b3)
HS2: Gii bi tp 29b/6 SBT
Tnh nhanh:
872 + 732 272 132
= (872 272) + (732 132)
= (87 27) (87 + 27) + (73 13) (73 + 13)
= 60 . 114 + 60 . 86
= 60 (114 + 86)
= 60 . 200
= 12000
GV: cn cch no khc tnh nhanh bi tp trn:
HS: (872 132) + (732 272)
= (87 13) (87 + 13) + (73 27) (73 + 27)
= 74 . 100 + 46 . 100
= (74 + 46) . 100 = 12000
GV: Nhn xt, ghi im
- Qua bi tp ny ta thy phn tch a thc thnh nhn t cn c thm phng php nhm cc hng t.
( GV gii thiu bi mi
3. Bi mi:Hot ng ca thyHot ng ca trNi dung bi
- GV a v d 1 ln bng cho hc sinh thc hin, nu lm c th gio vin khai thc, nu khng lm c th gio vin gi cho hc sinh.HS tr li ming1. V d
( C th vn dng 2 phng php hc gii bi tp ny c khng?( Khng vn dng c v c 4 hng t khng c nhn t chung
( Trong 4 hng t, nhng hn t no c nhn t chung.( x2 v 3x; xy v 3y hoc x2 v xy; -3x v 3yV d1: Phn tch a thc sau thnh nhn t:
X2 3x + xy 3y
( Hy nhm cc hng t c nhn t chung v t nhn t chung cho tng nhm( x2 3x + xy - 3y
= (x2 3x) + (xy 3y)
= x(x 3) + y(x 3)Gii
( n y cc em c nhn xt g?( Gia 2 nhm li c nhn t chung l x 3x2 3x + xy 3y
= (x2 3x) + (xy 3y)
= x(x 3) + y (x 3)
= (x 3) (x + y)
Cch khc:
x2 3x + xy 3y
= (x2 + xy) + (-3x 3y)
= x(x + y) 3( x + y)
= (x y) (x 3)
( Hy t nhn t chung ca cc nhm( HS thc hin
( Em c th nhm hng t theo cch khc c khng?
( GV lu khi HS nhm cc hng t m t du - trc ngoc th phi i du tt c cc hng t trong ngoc
( GV gii thiu hai cch lm nh v d trn gi l phn tch a thc thnh nhn t gi l phng php nhm hng t. ( HS thc hin
- GV a v d 2: yu cu HS bng cc cch nhm khc nhau. Hy phn tch a thc thnh nhn t.- HS c lp cng thc hin
- 2 HS ln bng trnh byV d 2: Phn tch a thc sau thnh nhn t:
2xy + 3z + 6y + xz
gii
cch 1:
2xy + 3z + 6y + xz
= (2xy + 6y) + (3z = xz)
= 2y (x + 3) + z (3 + x)
= (x + 3) (2y + z)
Cch 2:
- GV hi: C th nhm (2xy + 3z) + (6y + xz) c khng? Ti sao?( HS: Khng. Vi nhm nh vy khng
phn tch c a thc thnh nhn t2xy + 3z + 6 + xz
= (2xy + xz) + (3z + 6y)
= x(2y + z) + 3 (z + 2y)
= (2y + z) (x + 3)
- GV: Vy khi phn tch a thc thnh nhn t bng phng php nhm hng t phi nhm thch hp, c th l:
+ Mic nhm u c th phn tch c.
+ Sau khi phn tch a thc thnh nhn t mi nhm th qu trnh phn tch phi tip thu c.
- GV lu : i vi mt a thc c nhiu cch nhm hng t. Cch lm nh cc v d trn gi l phn tch a thc thnh nhn t bng phng php nhm hng t.
** Ch : i vi mt a thc c th c nhiu cch nhm nhng hng t thch hp.
- GV cho HS lm 2. p dng:
( Cho HS lm vo v
( 1 HS ln bng trnh by- HS lm bi vo v, 1 HS ln bng thc hinTnh nhanh:
- GV cho HS quan st bi trn bng ph
( Gi HS nu kin ca mnh v li gii ca cc bn
( Gi 2 HS ln bng phn tch tip vi cch lm ca bn Thi v bn H.- HS: Bn An lm ng, bn Thi v bn H cha phn tch ht v cn c th phn tch tip c.
- 2 HS ln bng phn tch tip bi ca 2 bn Thi v H 15 .64 + 25 . 100 + 36 .15 + 60 .100
= 15(64 + 36) + 100 (25 + 60)
= 15 .100 + 100. 85
= 1500 + 8500
= 10000
4. Cng c:
Hot ng ca thyHot ng ca trNi dung bi
- Yu cu HS hot ng nhm, na lp lm bi 48b, na lp lm bi 48c/22 SGK
- GV lu HS
( Nu tt c cc hng t ca a thc c tha s chung th nn t tha s trc ri mi nhm
( Khi nhm, ch ti cc hng t hp thnh hng ng thc - HS hot ng theo nhm.
48b) 3x2 + 6xy + 3y2 3z2= 3(x2 + 2xy + y2 z2)
= 3 [(x + y)2 z2]
= 3 (x + y + z) (x + y z)
48c)
x2 2xy + y2 z2 + 2zt - t2)
=.
= (x y + z t) (x y z + t)
( i din cc nhm trnh by bi gii.
- GV kim tra bi lm mt s nhm.( HS nhn xt
- Cho HS nhn xt bi gii trn bng, gio vin nhn xt chung v sa sai (nu c).
5. Dn d:- Khi phn tch a thc thnh nhn t bng phng php nhm hng t cn nhm thch hp.
- n tp 3 phng php phn tch a thc thnh nhn t hc.
- Gii cc bi tp 47, 48a, 49, 50/22 SGK
- Gii cc bi tp 31, 32, 33/6 SBT
IV. RT KINH NGHIM TIT DY:.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
.......................................................................................................................................................................................................................................................................................................................... .......................................................................................................................................................................................................................................................................................................................... ............................................................................................................................................................. Tun:
Ngy son :
Ngy dy:
Lp:
Tit 12
LUYEN TAPI. MUC TIEU:
- KT: Ren luyen k nang giai bai tap phan tch a thc thanh nhan t bang cac phng phap:at tha so chung, dung hang ang thc ang nh, nhom cac hang t.
- KN: HS giai thanh thao loai bai tap nay, ong thi biet van dung mot cach linh hoat cac phng phap phan tch mot cach hp ly va nhanh chong.
- T: Gio dc tnh cn thn v chnh xc.
II. CHUAN B:
Phieu hoc tap, bang phu.
III. TIEN TRNH TIET DAY :
1).On nh :
2).Kiem tra : Kim tra trong lc luyn tp.
3).T chc luyn tp
Hoat ong cua ThyHoat ong cua TroNoi dung ghi
Giao vien cho hoc sinh trnh bay bai tap 48c/22 SGK.
GV:trong a thc nay co may hang t, e phan tch nhanh chung ta can ap dung phng phap nao?
Giao vien cho hoc sinh trnh bay bai tap 49b/22 SGK.
GV:Phai nhom nh the nao e tnh nhanh nhat?
Giao vien cho hoc sinh trnh bay bai tap 50/23 SGK.
GV: e tm x cac em bien oi ve trai nh the nao?
GV: Cho hoc sinh lam bai tap dang toan chia het o la bai 52/23 SGK.
GV: Hay bien oi a thc thanh mot tch?
Hoc sinh len bang trnh bay BT 48c/22 SGK.
HS: thc hien bai tap49b/22 SGK
HS t lam tren nhap va tra li ket qua bangnhom.
HS:Bien oi ve trai thanh mot tch va van dung kien thc A.B=0 khi A=0 hoac B = 0.
HS: Lam BT 52/24 SGK
HS: Bien oi a thc thanh mot tch trong o co mot tha so chia het cho 5.
HS: Len bang trnh bay bai lam.
BT 48/22 SGK:
c)x2-2xy+y2-z2+2zt-t2=( x2-2xy+y2)-( z2-2zt+t2)
=(x-y)2-(z-t)2=(x-y-z+t)( x-y+z-t).
BT49b/22 SGK:
Tnh nhanh
452+402-152+80.45
=(452+80.45+402)-152=(45+40)2-152=852-152 =70.100=7000.
BT50/23 SGK
b) 5x(x-3)-x+3 = 0
5x(x-3)-(x-3) = 0
(x-3)(5x-1) = 0
x-3 = 0 hoac5x-1=0
x = 3; x =.
BT52/24SGK:
C/M: (5n+2)2-4 chia het cho 5, nZ
Ta co:
(5n+2)2+4 =(5n+2+2)(5n+2-2)
=5n(5n+4) luon chia het cho5 nZ
4. Cng c:
Cho HS nhc li cc phng php lm i vi cc bi tp trn.
5). Dn d:
Bai tap:Phan tch cac a thc sau thanh nhan t
a) x2-2xy+y2-9
b) x2-3x+2IV. RT KINH NGHIM TIT DY
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..........................................................................................................................................................Tun:
Ngy son :
Ngy dy:
Lp:
Tit 13
9. PHN TCH A THC THNH NHN TBNG CCH PHI HP NHIU PHNG PHP
I. MC TIU: Kin thc : HS bit phn tch a thc thnh nhn t bng cch phi hp nhiu phng php.K nng : HS bit vn dng mt cch linh hot cc phng php phn tch a thc thnh nhn t hc vo vic gii ton phn tch a thc thnh nhn t.
Thi : Rn k nng quan st, tnh cn thn khi lm ton.II. CHUN B:
Thy: Bng ph ghi bi tp tr chi Thi Gii ton nhanh
Tr: Bng nhm
III. TIN TRNH TIT DY: 1. n nh 2. Kim tra: Gi 2 HS ln bng
HS1 gii bi 50b SGK
Tm x:
5x (x 3) x + 3 = 0
5x ( x - 3) ( x 3) = 0
( x- 3)(5x 1) = 0
=> x 3 = 0; 5x 1 = 0
=> x = 3; x =
HS2: Gii bi 32b/6 SBT (yu cu nhm theo 2 cch)
Phn tch a thc thnh nhn t:
C1: a3 a2x ay + xy
= (a3 a2x) (ay xy)
= a2 (a x) y(a x)
= (a x) (a2 y)
C2: a3 a2x ay + xy
= (a3 ay) (a2x xy)
= a2 (a2 y) x(a2 y)
= (a2 y) (a x)
GV nhn xt, ghi im
3. Bi mi:Gii thiu bi: Hi: Hy nhc li cc phng php phn tch a thc thnh nhn t hc?
GV: Trn thc t ta thng phi hp nhiu phng php ( gii thiu bi mi.
Hot ng ca thyHot ng ca trNi dung bi
- GV cho HS theo di v d 11. V d
( Vi bi ton trn em c th dng phng php no phn tch?- HS: t nhn t chung l 5x V d 1: Phn tch a thc sau thnh nhn t:
5x3 + 10x2y + 5xy2
( n y loi bi ton dng li cha? V sao?- HS: Cn phn tch tip c v trong ngoc l biu thc c dng (A + B)2gii:
5x3 + 10x2y + 5xy2= 5x (x2 + 2xy + y2)
= 5x (x + y)2
( Nh vy phn tch a thc 5x3 + 10x2y + 5xy2 thnh nhn t u tin ta dng phng php t nhn t u tin ta dng phng php t nhn t chung sau dng tip phng php dng HT
- GV cho HS quan st v d 2.HS:V d 2: Phn tch a thc sau thnh nhn t:
( v d ny, em c dng phng php t nhn t chung khng? Ti sao?- Khng, v c 4 hng t ca a thc khng c nhn t chung.x2 2xy + y2 9
gii
( Em nh dng phng php no? c th? HS: . Nhm cc hng t ri dng HT x2 2xy + y2 9
= (x2 2xy + y2) 9
= (x y)2 - 32= (x y+3)(xy 3)
( GV cho HS quan st trn bng ph cc cch nhm:
x2 2xy + y2 9
= (x2 2xy) + (y2 9)
Hoc
- (x2 2xy) + (y2 2xy) HS: Khng c v:
(x2 2xy) + (y2 9)
= x (x 2y) + (y 3) (y + 3)
th khng phn tch tip c
Hoc
=(x2 9) + (y2 2xy)
= (x 3) (x + 3) + y(y 2x) cng khng phn tch tip c
( GV nu mt s bc quan trng trong khi phn tch a thc thnh nhn t.
- t nhn t chung nu cc hng t u c nhn t chung.
- Dng HT nu c
- Nhm nhiu hng t (thng mi nhm c nhn t chung hoc l dng HT) nu cn thit phi t du - trc ngoc v i du cc hng t.
- Yu cu HS lm - HS lm bi vo v
- 1 HS ln bng lm
2x3y 2xy34xy2 2xy
= 2xy(x2y2 2y 1)
= 2xy[x2(y2 +2y + 1)]
= 2xy [x2 (y + 1)2]
= 2xy(xy1)(x+y+ 1)
-Cho HS thc hin theo nhm phn a
( GV cho cc nhm kim tra kt qu lm ca nhm mnh.
.GV cho HS cu b) trn bng ph. Yu cu HS ch r cch lm ca bn Vit dng nhng phng php no phn tch a thc thnh nhn t.
- HS hot ng nhm phn a
( Phn tch x2 + 2x + 1 y2 thnh nhn t:
..= (x + 1 + y) ( x + 1 y)
( Thay x = 94,5; y = 4,5 vo a thc sau khi phn tch ta c:
----= 9100
( i din nhm trnh by)
- HS . Cc phng php nhm hng t, dng hng ng thc 2) p dng:
Tnh nhanh gi tr ca biu thc:
x2 + 2x + 1 y2
ti x = 94,5; y = 4,5
Gii:
Ta c: x2 + 2x + 1 y2 = ...
=(x + 1 + y) ( x + 1 y). Thay x = 94,5; y=4,5 ta c:
= ...
= 9100
4. Cng c:
Hot ng ca thyHot ng ca trNi dung bi
Cng c:
GV t chc cho HS thi lm ton nhanh.
: phn tch a thc thnh nhn t v nu cc phng php m i mnh dng
i 1: 20z25x210xy 5y2i 2: 2x 2yx2+2xy y2Yu cu: Mi i gm 5 HS. Mi HS ch c vit 1 dng (trong qu trnh phn tch a thc thnh nhn t) HS cui cng vit cc phng php m i mnh dng khi phn tch. HS sau c quyn sa sai ca HS trc. i no lm nhanh v ng l thng.Kt qu:
i 1: 20z25x210xy 5y2= 5(4z2 x22xy y2)
= 5[(2z)2 (x + y)2]
= 5(2zxy)(2z+x+ y)
Phng php: t nhn t chung nhm hng t, dng HT
i 2:
2x 2y x2 + 2xy y2=(2x2y)(x22xy+ y2)
= 2 (x y) ( x y)2= ( x y) [2 (x y)]
= ( x y) (2 x + y)
- Sau cng GV cho HS nhn xt, cng b i thng cucPhng php: nhm hng t, dng HT, t nhn t chung.
5. Dn d:- n li cc phng php phn tch a thc thnh nhn t
- Gii cc bi tp 52, 54, 55/25 SGK + 34/7 SBT
- Nghin cu phng php tch hng t phn tch a thc thnh nhn t qua bi tp 53/24 SGK.
IV. RT KINH NGHIM TIT DY:.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
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Tun:
Ngy son :
Ngy dy:
Lp:
Tit 14
LUYN TP (9)
I.MC TIU:- KT: Rn luyn k nng gii bi tp phn tch a thc thnh nhn t.
- KN: HS gii thnh tho loi bi tp phn tch a thc thnh nhn t .
- T: Cng c, khc su, nng cao k nng phn tch a thc thnh nhn t.
II.CHUN B:Thy: Bng ph ghi sn bi tp 53a
Tr: Bng nhmIII. TIN TRNH TIT DY:1. n nh 2. Kim tra: gi 2 HS ln bng
HS1: Gii bi tp 51 a, (SGK)
Phn tch a thc thnh nhn t:
a) x3 2x2 + x = x(x2 2x + 1) = x (x 1)2b) 2x2 + 4x + 2 2y2 = 2 (x2 + 2x + 1 y2) = 2 [(x2 + 2x + 1) y2) =.
= 2 (x + 1 + y) (x + 1 y)
HS2: Gii bi tp (SGK)
Chng minh rng (5n + 2)2 4 chia ht cho 5 vi mi s nguyn n.
Ta c: (5n + 2)2 4 = (5n + 2)2 - 22 = (5n + 2 2) (5n + 2 + 2) = 5n (5n + 4)
Vy... lun chia ht cho 5 vi mi n(Z
- GV nhn xt cho im
- Hi: Khi phn tch a thc thnh nhn t ta tin hnh nh th no?
(p:
- t nhn t chung nu tt c cc hng t c nhn t chung .
- Dng hng ng thc (nu c)
- Nhm nhiu hng t (thng mi nhm c nhn t chung hoc l hng ng thc); cn thit phi t du - trc du ngoc v i du hng t trong ngoc.
3. T chc luyn tp:Gii thiu bi: Trong tit ny chng ta s lm mt s bi tp cc em nm vng pp phan tch a thc thnh nhn t.Hot ng ca thyHot ng ca trNi dung bi
+ Cho HS lm bi tp 54/251. Bi tp 54/25 (SGK)
- Gi 3 HS ln bng (mi HS lm 1 phn)+ 3 HS ln bng thc hin theo yu cu GV a)x3 + 2x2y + xy2 9x
= x (x2 + 2xy + y2 9)
=..
= x(x + y +3)(x + y 3)
b) 2x 2y x2+2xy y2= 2 (x y) (x y)2= (x y) (2 x + y)
- Yu cu HS nhn xt sa sai (nu c)- HS nhn xt ..c) x4 2x2 = x2 (x2 2)
= x2 (x + ) (x - )
+ Cho HS lm bi 55(a, b) trang 25/SGK 2. Bi tp 55/25 (SGK)
a) x3 - x = 0
- GV yu cu HS suy ngh v hix (x2 - ) = 0
- tm x trong bi ton trn em lm th no?HS: phn tch a thc v tri thnh