|
(254
—
255):
254.
1)
+
+
x
x
x
1
1
1
3
2
6
;
3)
-
+
-
y
y
y
y
4
4
4
4
3
1
1
1
2
16
32
4
;
2)
-
-
y
y
y
5
1
1
6
3
6
;
4)
-
+
-
a b
a b
a b
a b
2
2
2
2
3
5
1
3
2
8
8
16
.
255.
1)
2
4 ;
+ + -
m q q
m
3)
+
+
-
2
2
x
y
x
y
2
2
3
4
;
2)
3
2
;
+
- -
a
b b a
4)
2
2
5
4
3
.
-
-
+
a
b
a
b
2
2
2
2
2
2
2
2
2
3
4
5
a bc
a c
a b
a c a b a bc
=
-
-
+
+
-
=
M a s h q l a r
80
Ko‘phadni standart shaklga keltiring
(256—261):
256.
1)
11
4
4 ;
+
-
-
x
x x
x
2
2
3)
2
0,1
0,5 ;
-
-
2
3
0,3
c
c
c
2)
2
3
2
2 ;
-
+
-
y
y
y
y
2
2
4)
2
1,2
3,4
0,8 .
+
-
a
a
a
2
2
257.
1)
-
+
+
2
2
x
y
x
y
1
1
2
1
3
3
3
3
;
2)
+
+
-
2
2
2
2
a
b
a
b
1
3
4
3
5
4
5
4
;
3)
2
0,7
5
8 ;
+
-
+
2
2
1,2
ab
b
ab+
b
ab
4)
5
3,5
2
.
-
-
-
xy
y
xy +
y
xy
2
2
1,3
258.
1)
-
+
+
-
-
2
2
x
xy
x y xy
x y
y
3
2
5
1
4
3
6
2
;
2)
-
+
-
-
2
2
2
2
a
a
ab
b
a b
b
2
1
7
3
3
1
2
8
4
8
2
;
a b
3)
3,89
8,197
0,81 ;
-
-
-
-
9,387
1,11
a
b+
a
b
a
4)
-
-
+
+
8,53
4,73
5,12
2,27
0,59 .
x
y
x
y
x
259.
1)
-
+
-
+
2
2
2
2
2
2
2
8
5
5
3
4 ;
a b
b
a b+ c
b
c
2)
2
3
2
3
2
2
8
4
5
3
4
9
;
xy
x
x y
x
x y
xy
+
-
-
+
-
3)
+
-
+
-
+
2
3
2
3
1
3
2
6
3
3
7
8
5
7
8
5
;
ab
a
b
ab
a
b
4)
-
+
+
+
-
+
2
3
2
3
3
3
2
1
8
2
3
1
5
3
4
3
5
4
2
.
ab
ab
a
ab
ab
a
a
260.
1)
( )
-
-
-
-
5 3
4 3
5 2
4
2 ;
b b
c b
b c
c
c
2)
8
3 8
5
3 5 ;
b b
c b+ cb
c c
-
-
3)
+
-
-
2
2
2
2
2
2
2
2
6 2
5 2
6 4
5 4 ;
a a
b a
a b
b b
4)
-
+
+
2
2
1
1
1
4
2
3
4
5
2
3
1
.
x
y
ab a
y x
aab
261.
1)
-
+
+
2
2
2
1
3
1
9
24
;
4
a
b a b
a
c
2)
-
-
2
1
3
2
4
;
ab ac
aca a bc
3)
-
+
+
2
2
1
1
4
2
3
5
4
9
4
;
x
y
ab a
y x
aba
4)
(
)
+
-
-
2
2
1
2
1
1
1
2
3
4
3
15
5
0,5
.
a b
a
b
5b
a
a
ab
81
Ko‘phadlarni qo‘shish va ayirish
O‘lchamlari 11- rasmda ko‘rsatilgan
uchburchakni qaraymiz. Uning
P
peri-
metri tomonlar uzunliklarining yig‘in-
disiga teng:
P
= (2
a
+ 3
b
) + (4
a
+
b
) + (2
a
+ 4
b
).
Bu ifoda quyidagi uchta ko‘phadning yi-
g‘indisidir:
2
a
+ 3
b
, 4
a
+
b
, 2
a
+ 4
b
.
Qavslarni ochish qoidasiga ko‘ra bunday
yozish mumkin:
P
= 2
a
+ 3
b
+ 4
a
+
b
+ 2
a
+ 4
b
.
O‘xshash hadlarni ixchamlasak,
P
= 8
a
+ 8
b
tenglik hosil bo‘ladi.
Ko‘phadlarning istalgan algebraik yig‘indisi ham xuddi
shunga o‘xshash soddalashtiriladi, masalan,
(
) (
)
2
2
2
2
2
2
2
2
2
2
2
2
2
3
2
3
3 ;
n
m
n
m
q
n
m
n
m
q
n
q
-
-
-
+
=
-
-
+
-
=
-
(
) (
) (
)
3
4
3
b
-
+
-
-
-
=
ab
c
bc ab
ac
bc
3
4
3
2
.
=
-
+
-
-
+
=
-
ab
bñ bc ab ac
bc
ab ac
Bir nechta ko‘phadlarni qo‘shish va ayirish natijasida yana
ko‘phad hosil bo‘ladi.
Bir nechta ko‘phadning algebraik yig‘indisini standart
shakldagi ko‘phad ko‘rinishida yozish uchun qavslarni ochish
va o‘xshash hadlarni ixchamlash kerak.
Ba’zi ko‘phadlarning yig‘indisi yoki ayirmasini sonlarni
qo‘shish va ayirishga o‘xshash „ustun“ usulida topish qulay
bo‘ladi. Bunda o‘xshash hadlar birining ostiga ikkinchisi tura-
digan qilib yoziladi, masalan,
11- rasm.
a
a
a
a
b
b
b
b
b
a
a
15-
b
b
b
a a
6 — Algebra, 7- sinf
82
1) +
-
+
-
-
-
5
4
3
3
7
;
5
4
a
bc
ac
bc
ac
a bc
ac
2)
-
-
+
-
-
-
+
+
-
5
2
4
3
3
3
.
2
5
4
abc
ab
ac bc
abc
ab ac
bc
abc ab+ ac
bc
Ko‘phadlarning algebraik yig‘indisini toping
(262
—
267):
262.
1)
(
)
8
3
5 ;
a
b
a
+ -
+
3)
(
)
(
)
-
-
+
6
2
5
3 ;
a
b
a
b
2)
(
)
5
2
3
;
x
x
y
-
-
4)
(
) (
)
4
2
1 .
x
x
+
+ - -
263.
1)
(
)
2
2
3
4
2
;
x
x
y
-
+
3)
(
)
2
2
0,6
0,5
0,4 ;
a
a
a
-
-
2)
(
)
2
2
2
2
3
;
a
b
a
-
-
4)
-
-
2
2
1
1
2
4
.
1
2
1
b
b
264.
1)
2
3
3
1
3
5
4
4
5
1
;
-
+
-
2
2
b
b
b
b
2)
(
) (
)
2
2
0,1
0,4
0,1
0,5
;
c
c
c
c
-
-
-
3)
(
) (
)
13
11
10
15
10
15 ;
x
y +
z
x
y
z
-
- -
+
-
4)
(
) (
)
17
12
14
11
10
14 .
a
b
c
a
b
c
+
-
-
-
-
265.
1)
(
) (
)
2
2
2
2
7
4
2
;
m
mn n
m
mn n
-
-
-
-
+
2)
(
) (
)
2
2
2
2
5
11
8
2
7
5
;
a
ab
b
b
a
ab
-
+
+ -
-
+
3)
(
) (
)
+
+
-
+
-
2
2
11
13
17
10
10
3
;
ac
bc
b
ac
bc
b
4)
(
) (
)
+
+
-
+
-
2
2
41
13
26
16
13
4
.
z
az
az
z
az
az
266.
1)
(
)
+
-
-
+
+
1
a
a
b
a b
1
5
2
2
3
2
3
;
b
2)
(
) (
) (
)
0,3
1,2
1,3
0,2 ;
a
b
a b
a
b
-
+
- -
-
3)
(
) (
) (
)
-
-
-
+ -
-
3
2
3
2
2
3
11
2
5
3
;
p
p
p
p
p
p
4)
(
) (
) (
)
+
+
-
- -
+
2
3
3
2
3
2
5
6
2
4
.
x
x
x
x
x
x
267.
1)
(
) (
) (
)
3
2
2
2
2
3
2
1
3
;
-
+
+
-
+
-
+
x
xy
x y
x y xy
x
2)
(
) (
) (
)
2
2
2
2
3
5
7
5
3
7
3
;
+
+
-
+
-
-
x
xy
x y
xy
x
x y
x
2
M a s h q l a r
83
3)
(
) (
) (
)
2
2
2
2
2
8
10
6
2
8
4
;
-
-
+ -
+
-
-
-
+
a
ab b
a
ab b
a
ab
b
2
4)
(
) (
) (
)
2
2
2
2
2
2
4
2
2
3
.
a
-
-
- - +
-
+
+
-
a
b b
a
b
ab
a
b
ab
268.
Ko‘phadlarning yig‘indisi va ayirmasini toping:
1)
+
-
2
2
2
2
0,1
0,02
va 0,17
0,08 ;
x
y
x
y
2)
-
-
+
2
2
2
2
0,1
0,02
va 0,17
0,08 ;
x
y
x
y
3)
-
-
3
3
3
3
0,12
va 0,39
;
a
b
a
b
4)
+
-
+
3
3
3
3
0,12
va 0,39
.
a
b
a
b
269.
Ko‘phadlarning yig‘indisini „ustun“ usulida toping:
1)
+
-
-
2
2
2
3
2
va 2
3 ;
ab a
b
a
ab
2)
+
-
-
+
-
2
2
2
2 2
3
3
2
4
va 4
2
3
.
x
xy
y
y
xy
x y
x
270.
Ko‘phadlarning ayirmasini „ustun“ usulida toping:
1)
+
-
+
-
2
2
3
8
4 va 3 8
5 ;
a
a
a
a
2)
-
+
+
3
2
2
3
3
4 va
2
.
b
b + b
b
b
b
271.
1) Agar
P
= 5
a
2
+
b
,
Q
=
-
4
a
2
-
b
bo‘lsa,
P
+
Q
ifoda
nimaga teng?
2) Agar
P
= 2
p
2
-
3
q
3
,
Q
= 2
p
2
-
4
q
3
bo‘lsa,
P
-
Q
ifoda
nimaga teng?
3) Agar
A
=
a
2
-
b
2
+
ab
,
B
= 2
a
2
+ 3
ab
-
5
b
2
,
C
=
-
4
a
2
+
+ 2
ab
-
3
b
2
bo‘lsa,
A
+
B
+
C
ni toping;
4) Agar
A
= 2
a
2
-
3
ab
+ 4
b
2
,
B
= 3
a
2
+ 4
ab
-
b
2
,
C
=
a
2
+
+ 2
ab
+ 3
b
2
bo‘lsa,
A
-
B
+
C
ni toping.
272.
Isbotlang:
1) beshta ketma-ket natural sonning yig‘indisi 5 ga bo‘li-
nadi;
2) to‘rtta ketma-ket natural sonning yig‘indisi 4 ga bo‘lin-
maydi;
3) to‘rtta ketma-ket toq natural sonning yig‘indisi 8 ga
bo‘linadi;
4) to‘rtta ketma-ket juft natural sonning yig‘indisi 4 ga
bo‘linadi.
273.
Avtobusda
n
nafar yo‘lovchi bor edi. Dastlabki ikki
bekatning har birida
m
nafardan yo‘lovchi avtobusdan
84
tushdi, uchinchi bekatda esa hech kim tushmadi, lekin
bir necha kishi avtobusga chiqdi, shundan so‘ng avtobus-
dagi yo‘lovchilar soni
k
nafar bo‘ldi. Uchinchi bekatda
avtobusga necha kishi chiqqan?
Do'stlaringiz bilan baham: |
