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
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