|
(395
—
396):
395.
1)
48 52;
×
2)
68 72;
×
3)
43 37;
×
4)
47 53.
×
396.
1)
×
27 33;
2)
44 36;
×
3)
84 76;
×
4)
201 199.
×
118
397.
Soddalashtiring:
1)
(
) (
)(
)
-
-
+
-
2
3
3 3
;
c
c
c
2)
(
) (
)(
)
+
-
+
-
2
2
2 2
;
a
a
a
3)
(
)(
) (
)
+
-
+
+
2
2
3
2
3
2
3
;
x
y
x
y
x
y
4)
(
)(
) (
)
-
+
-
-
2
3
4
3
4
3
4
;
a
b
a
b
a
b
5)
(
)(
)
- -
+
+
+
2
2
;
b a a b
a
b
6)
(
)(
)
-
- -
+
2
2 .
b a
a b
b
398.
Ifodaning qiymatini toping:
1)
(
) (
)(
)
-
+
+
-
+
= -
2
4
3
3
3 , bunda
2,4;
m
m
m
m
m
2)
(
)
(
)(
)
+
-
-
-
+
= -
2
3
4
10
4 4
, bunda
0,1;
x
x
x
x
x
3)
(
)(
) (
) (
)(
)
-
+
-
-
-
-
+
= -
2
1
2
2
7
5
5
7 7
, bunda
;
k
k
k
k
k
k
4)
(
) (
)(
)
(
)(
)
+
+
-
+
-
+
-
= -
2
1
5
3
3 3
2
2
4 , bunda
.
a
a
a
a
a
a
399.
Tenglamani yeching:
1)
(
)
(
)(
)
+
-
-
+
=
2
2
3
4
1
1
49;
x
x
x
2)
(
) (
)(
)
+
-
-
+
=
2
3
4
3
1 1 3
49;
x
x
x
3)
+
-
-
=
3
2
2
9
18 0;
x
x
x
4)
-
-
+
=
3
2
3
4
12 0.
y
y
y
400.
Kvadratning ikki qarama-qarshi tomonining har biri
8 sm ga uzaytirildi, qolgan ikki tomoni esa shuncha qis-
qartirildi. Shaklning yuzi qanday o‘zgardi?
401.
Hisoblang:
×
- ×
×
×
4
3
5 0,128 5 0,628 5 .
125 0,25
119
Ko‘phadni ko‘paytuvchilarga ajratishning bir
necha usulini qo‘llash
Ko‘phadni ko‘paytuvchilarga ajratishda ba’zan bir emas,
balki bir necha usullar qo‘llaniladi. Misollar keltiramiz:
1)
a
3
-
a
ko‘phadni ko‘paytuvchilarga ajrating:
(
)
(
) (
)
3
2
1
1
1 .
a
a a a
a a
a
- =
- =
-
+
Bu yerda ikkita usuldan foydalanilgan: umumiy ko‘paytuvchini
qavsdan tashqariga chiqarish va kvadratlar ayirmasi formula-
sini qo‘llash.
2) (
a
2
+1)
2
-
4
a
2
ko‘phadni ko‘paytuvchilarga ajrating:
(
)
(
)
( )
(
)
(
)
(
)(
) (
)(
)
(
) (
)
+
-
=
+
-
=
+ -
+ +
=
=
+ -
+ +
=
-
+
+
+ =
=
-
+
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
4
1
2
1
2
1
2
1 2
1 2
2
1
2
1
1
1 .
a
a
a
a
a
a
a
a
a
a a
a
a
a
a
a
a
a
Bu yerda qo‘shiluvchilar umumiy ko‘paytuvchiga ega emasligi
sababli, avval kvadratlar ayirmasi formulasidan foydalanildi,
so‘ngra yig‘indi va ayirma kvadratlarining formulalaridan foy-
dalanildi. Yana bir misol yechib ko‘raylik:
3)
(
)
(
)
(
)(
)
(
) (
)(
)
-
+
+
=
-
+
+
=
=
-
+
+
+
=
+
- +
2
2
2
2
4
4
2
4
4
2
2
2
2 2
2
2
2 .
x
y
x
y
x
y
x
y
x y
x y
x y
x y
x y
Birhadlar umumiy ko‘paytuvchiga ega bo‘lmagani va biror
formulani qo‘llash mumkin bo‘lmagani uchun, bu yerda avval
guruhlash usulidan foydalanildi, so‘ngra esa kvadratlar ayir-
masi formulasi qo‘llanildi.
Ko‘rib chiqilgan bu misollar ko‘phadni ko‘paytuv-
chilarga ajratishga doir topshiriqlarni bajarishda quyidagi
tartibga rioya qilish foydali ekanligini ko‘rsatadi:
1) umumiy ko‘paytuvchini (agar u bor bo‘lsa)
qavsdan tashqariga chiqarish;
23-
120
2) ko‘phadni qisqa ko‘paytirish formulalari bo‘yicha
ko‘paytuvchilarga ajratishga urinib ko‘rish;
3) agar oldingi usullar maqsadga olib kelmasa, gu-
ruhlash usulini qo‘llashga harakat qilish.
Masala.
Tenglikni isbotlang:
(
)
(
)
3
3
2
2
.
a
b
a b a
ab b
+
=
+
-
+
(1)
Tenglikning o‘ng tomonidagi qavslarni ochamiz:
(
)
(
)
2
2
3
2
2
2
2
3
3
3
.
a b a
ab b
a
a b ab
a b ab
b
a
b
+
-
+
=
-
+
+
-
+
=
+
Tenglikning o‘ng tomoni chap tomoniga tengligi kelib chiqdi,
ya’ni (1) tenglik isbot qilindi.
Xuddi shu kabi
(
)
(
)
3
3
2
2
a
b
a b a
ab b
-
=
-
+
+
(2)
tenglikning to‘g‘riligi isbotlanadi.
(1) va (2) tengliklar, mos ravishda,
kublar yig‘indisi
va kublar ayirmasi formulalari
deb ataladi. Bu formulalar
ham ko‘phadni ko‘paytuvchilarga ajratishda qo‘llaniladi.
Masalan:
(
)
(
)
(
)
( )
(
)
(
)
+
=
+
= +
-
+
-
=
-
=
-
=
-
+
+
3
3
3
2
3
4
3
3
3
3
2
2
1) 27
3
3
9 3
;
2)
8
8
2
2
2
4
.
b
b
b
b b
x
xy
x x
y
x x
y
x x
y x
xy
y
402.
Hisoblang:
1)
-
2
2
47
37 ;
2)
-
2
2
54
44 ;
3)
-
2
2
50,7
50,6 ;
4)
-
2
2
29,4
29,3 .
403.
(Og‘zaki.) Ko‘paytuvchilarga ajrating:
1)
-
2
36
;
x
2)
-
2
25;
a
3)
-
2
1;
y
4)
-
2
1
.
b
M a s h q l a r
121
404.
1)
(
)
+
=
+
2
2
2
2
4 ;
a
b
a
b
2)
(
)
-
=
-
2
2
2
2
3
4
9
a
b
a
b
tengliklar haqida nima deya olasiz?
a
)
ular qaysi
a
va
b
larda to‘g‘ri-yu, qaysilarida noto‘g‘ri?
b
) ixtiyoriy
a
va
b
lar uchun ularni to‘g‘ri bo‘ladigan
qilishni uddasidan chiqasizmi?
Ko‘paytuvchilarga ajrating
(405
—
416):
405.
1)
-
2
25
9;
x
2)
-
2
4
9;
a
3)
-
2
2
64
36 ;
y
x
4)
-
2
2
81
16 .
a
b
406.
1)
-
2
2
9;
c d
2)
-
2 2
16;
a b
3)
-
2
2
4
9 ;
a
b
4)
-
2
2
16
25 .
x
y
407.
1)
-
2
2
1
16
9
25
;
y
x
3)
-
2
2
0,25
49 ;
a
b
2)
-
2
2
4
1
9
16
;
a
b
4)
-
2
2
0,09
16 .
x
y
408.
1)
-
2
2
36
1;
x y
2)
-
2
4
16;
x y
3)
-
6
4
81
49 ;
a
b
4)
-
2
6
25
9 .
a
b
409.
1)
-
4
4
;
a
b
2)
-
4
8
;
a
b
3)
-
4
16;
a
4)
-
4
81.
b
410.
1)
(
)
+
-
2
2
;
a b
c
3)
(
)
+
-
2
2
2
9 ;
a
b
a
2)
(
)
-
-
2
2
;
m n
k
4)
(
)
-
-
2
2
3
4 .
x y
y
411.
1)
(
) (
)
+
-
-
2
2
;
a b
a c
3)
(
) (
)
+
-
+
2
2
2
2
;
a b
b a
2)
(
) (
)
+
-
+
2
2
;
a b
b c
4)
(
) (
)
-
-
+
2
2
3
3
.
a
b
a b
412.
1)
-
+
2
9
6
1;
a
a
3)
+
+
2
36
12
1;
b
b
2)
+
+
2
1 2
;
c c
4)
2
81 18
.
x x
-
+
413.
1)
+
+
2
9
24
16;
x
x
3)
+
+
2
2
36
12
;
m
mn n
2)
-
+
2
100 60
9 ;
a
a
4)
+
+
2
2
10
25 .
a
ab
b
414.
1)
+
+
4
2
2
2
;
x
x y y
3)
+
+
4
2 3
6
4
12
9 ;
c
c b
b
2)
-
+
4
2
2
2
;
p
p q q
4)
+
+
6
3
2
25
30
9 .
a
a b
b
415.
1)
-
+
4
2
8
16;
a
a
3)
-
+
4
2
2
25
10
;
a
a b b
2)
-
+
4
2
18
81;
b
b
4)
-
+
2 2
4 4
16 8
.
a b
a b
122
416.
1)
- -
-
2
2
1;
a
a
3)
-
+
-
2
2
2
8
8 ;
a
ab
b
2)
- +
-
2
9 6
;
b b
4)
-
-
-
2
2
12
3
12 .
ab
a
b
417.
Ifodaning son qiymatini toping:
1)
-
+
=
=
2
2
5
10
5 , bunda
142,
42;
m
mn
n
m
n
2)
+
+
=
=
2
2
6
12
6 , bunda
56,
44;
m
mn
n
m
n
3)
-
+
-
=
=
3
2
2
1
9
36
4
, bunda
4,
48;
a
a b
ab
a
b
4) –
-
-
= -
=
3
2
2
1
4
64
8
, bunda
6,
84.
a
a b
ab
a
b
418.
Tenglamani yeching:
1)
-
=
2
36 0;
x
3)
+
+ =
2
4
4
1 0;
x
x
2)
-
=
2
1
4
0;
x
4)
-
+
=
2
25 10
0.
x x
419.
Hisoblang:
1)
-
×
+
2
2
101
202 81 81 ;
3)
+ ×
×
+
-
2
2
2
2
48
2 48 18 18
48
18
;
2)
+
×
+
2
2
37
126 37 63 ;
4)
-
+ ×
×
+
2
2
2
2
85
17
85
2 85 17 17
.
420.
Tushirib qoldirilgan shunday uchhadni topingki, tenglik
bajarilsin:
1)
(
) ( )
+
=
+
3
3
... ;
x
y
x y
3)
(
) ( )
-
=
-
3
3
... ;
x
y
x y
2)
(
) (
) ( )
+
=
+
3
... ;
x y
x y
4)
(
) (
) ( )
-
=
-
3
... .
x y
x y
421.
Ko‘paytuvchilarga ajrating:
1)
-
3
3
;
x
y
3)
+
3
27;
x
5)
-
3
64;
n
7)
-
3
1
;
p
2)
+
3
3
;
c
d
4)
-
3
27;
a
6)
+
3
1;
a
8)
-
3
125
.
b
Ko‘paytuvchilarga ajrating
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