Sh. A. Alimov, O. R. Xolmuhamedov, M. A. Mirzaahmedov

a²b³c, bunda a = -2, b = -1, с = 10.

A) B) j; C) -8; D) 8; E) -40.

4. 
   B
   C) -j6V;
   
   B) -я³6³; 3
   E) -2я³6³.
   irhadni standart shaklda yozing: 2*ab² j a b
   

A) 2aa²b²b',
D) 4я³6³;

\f Q N
— a£rc

--a’iV 15

14

/V

97

5* Birhadlami ko‘paytiring:
OO 7 — Algebra, 7- sinf " "■ ■

А) 0,3a’fcV; В) -0,3(e6c)⁴;
D
С) -^a'bVb²-,
) — a⁴c⁴b³; E) to‘g‘ri javob berilmagan.

6. 
   Ko‘phadni uning har bir hadini standart shaklga keltirib, soddalashtiring: 3b²a5ab - 6b² Aaba + abAab².
   

1. 
   43 a³b³; B) 43a²V; C) -5a³6²;
   

4. 
   -5a²b³; E) 5a²6³.
   

6. 
   K

   0,5 a + -b	(7 i A - -a--b
   ^3 >	I^2 3 ,

   
   A) a + 36;
   o'phadlaming algebraik yig‘indisini toping:
   

+ 2(a + b).
В) -a+ 36; C) -a-3b; D) a-3b;

4. 
   бя + 2-б. ⁷ 2
   

, 1
4я--л:
3

(~3x).
C) 3x²+\2ax;

8. Ko'phadni birhadga ko‘paytiring:
A) -\lax-3x²; B) 3x²-I2ax;

D) x²-12ax;

9. Soddalashtiring: 5я(0,4я-6)-4я

E) —jc² +12 ax.

-a-b
4

A
C) a²+9ab;
) я(я-6); B) я(я + 6);
D) 3a² + 9ab; E) 3a²-ab.

10. 
    Ko‘phadni standart shaklga keltiring:
    

4
-I — 11

ac.
я6сЗя-2-6²1 —яс-3-яб 7 19 3 ,2 j.„ о „ 1.2 r>\ -3 „1.2
A) I2a²bc-Sab с; B) \la^Lbc-3ab с; C) -\2a²bc-3ab²c; D) 12я²6с-3я6²с; E) 17я²6с + 3я6²с.

10. 
    Ko‘phadlami ko‘paytiring: (я-6)(я + 6)(я² +b²).
    

A) a³ -b⁴; B) я⁴+6³; C) a³-b³;
D
E) a⁴+b⁴
) a'-b⁴;

10. 
    Bo‘lishni bajaring: (16a³b² -4a²b + a² b²): (4a²b²).
    

A) 4a + b + -; B) 4a + b + 4; C) 4ab-- + 4\

3. 
   6
   

D) 4a-46+ 4; E) 4a-b + ^.

10. 
    Algebraik ifodaning son qiymatini toping:
    

3
(10a⁴ + 15a³): 5a² -18a³: (-6a), bunda « =
A) -15,75; B) 6,75; C) 15,75; D) -12; E) 18.
( l⁴

10. 
    Ifodani soddalashtiring: (18a⁴ + 21a²): 3a² -5a 2 a + -
    

A) 4a² + 2; B) 16a² +12; C)-4a²+2;
D) 16a² +2; E) -4a² + 12.

10. 
    Ko‘phadlami ko‘paytiring: (a + 2b)(a-2b)(a²+4b²).
    

A) a³ -166³; B) a⁴ -86³; C) a³-86³;
D) а⁴ +166⁴; E) a⁴-16Z>⁴.
Hisoblang: (16—20):
(-0,2)⁵
1
\4 *

(-0ДГ A) -3,2;
D) -0,00032;
6.

100. 
     0
     B) 3,2; E) -1.
     
     П
     ,00032;
     

17. 
    -(-3)³
    

E) -9.

C) -2,7;

°) 9’

B) 3;

18.

D) 5,2; E) 16.

B) 8,32; C) 83,2;

C) 10;

E) 2.

°)

в) j;

A) -3; (5,2)³
d,3)² ' A) 832;
10⁴ 2^s ■ 5⁴ A) 1;

• 
  • jc (-0,9)^², bunda х = -1, у = 10
  

18. 
    2
    

1. 
   -45; B) 45; C) -2,5; D) 2,5; E) 5.
   

22. Birhadni standart shaklda yozing:
( i \³
-
A) |*V;
- xV(-18)j>²*.
В) 18jc³j³; С) -18jcV;

2. 
   2
   E) 2xy.
   2
   

4. 
   -~x²yy²x;
   

& Tarixiy masalalar
(T) Nyuton masalasi. Bitta xattot 8 kunda 15 varaq yoza oladi. 405 varaqni 9 kunda yozib tugatish uchun nechta xattot kerak bo‘ladi?

2. 
   Yem otning o‘ziga 14 kunga, ot bilan toychoqqa esa 10 kunga yetadi. Shu yem toychoqning o‘ziga necha kunga yetadi?
   

(5) Asalarilaming beshdan biri oq gullarga, uchdan biri esa qizil gullaiga qo‘ndi. Ular ayirmasining uch baravari esa sariq gullardan bol yig‘moqda. Faqat bittagina asalari gullar iforidan rohatlanib, uchib yuribdi. Qani menga ayt-chi, gulzorda qancha asalari bor?
Ш Tarixiy ma’lumotlar
Noma’lum kattaliklami harflar bilan belgilash mashhur yunon matematigi Diofant (III asr) asarlaridayoq uchraydi. Koeffitsiyentlami ham, ma’lum miqdorlami ham harflar bilan belgilashni F.Viyet (1540— 1603) birinchilardan bo'lib qo‘llagan. Algebraik tenglamalarni umumiy 100
holda tadqiq qilish harfiy koeffitsiyentlar kiritilgandan keyingina mumkin bo‘ldi. F. Viyet undosh bosh lotin harflari — B, G, D, ... bilan koeffitsiyentlami, unli harflari — A, E, I, ... bilan esa noma’lumlami belgilagan. Mashhur fransuz matematigi va faylasufi R. Dekart (1596— 1650) koeffitsiyentlami belgilash uchun lotin alifbosining dastlabki (kichik) harflari a, b, c, d, ... dan, noma’lumlami belgilash uchun esa alifboning oxirgi harflari x, y, z lardan foydalangan. Darajaning hozirgi zamonaviy belgilanishi a¹, o³, aⁿ (n— natural son)ni ham Dekart kiritgan (1637-yil).
„Al-jabr val muqobala“ asarining ,,Ko‘paytirish haqida bob“ida al-Xorazmiy birhadlami ko‘paytirishga, ikkihadni ikkihadga ko‘paytirishga hamda soddalashtirishga doir misollarni qaraydi. Al- Xorazmiy misollaridan ba’zilarini keltiramiz:

1. 
   (IO-jc)jc;
   
2. 
   (10 +jc)(10 +x);
   
3. 
   (10-a)(10-jc);
   
4. 
   (10 — jc)(10 + x);