ÇARPAN LARA AYIRM A

A. ORTAK ÇARPAN PARANTEZĞNE ALMA
A(x) . B(x) ± A(x) . C(x) = A(x) . [B(x) ± C(x)]
En azdreioan iadlrotaran pareiÚakbimde

öttrmilfeerakçpantznealnacç
i
rpandrÚ

gulÚl,oa otaran pareiÚr
ÚrsnrrakçpantznealnÚ.,
B. ÖZDEğLĞKLER rakÚ-ToplmÚ1. ĞkiKaeFra
i. a2 œ b2 = (a œ b) (a + b)
ii. a2 + b2 = (a + b)2 œ 2ab ya da
i.
a2 + b2 = (a œ b)2 + 2ab dr
akÚ-ToplmÚ
2. ĞkiKüpFra
i. a3 œ b3 = (a œ b) (a2 + ab + b2 )
ii. a3 + b3 = (a + b) (a2 œ ab + b2 )
iii. a3 œ b3 = (a œ b)3 + 3ab (a œ b)
iv. a3 + b3 = (a + b)3 œ 3ab (a + b)
rcdenFra
3. n. DeeeakÚ-ToplmÚ )nbiamasysomaküzr,irsyaÚÚlee
n n n œ 2 n œ 3 2 n œ 2 n œ 1
x œ y = (x œ y) (xn œ 1+ x y + x y +... + xy + y ) dr
i. i
)n bitksayÚÚlzr,
reayma ssomaküee
n n œ 2y+ xn œ 3y2

x + yn= (x + y) (xn œ 1œ x œ ... œ
n œ 2 n œ 1
xy + y ) dri.

ralr4. Tam KaeĞfdee
i. (a + b)2 = a2 + 2ab + b2
ii. (a œ b)2 = a2 œ 2ab + b2
2
iii. (a + b + c)2 = a2 + b2 + c + 2(ab + ac+ bc
)
iv. (a + b œ c2 )
)2 = a2 + b2 + c+ 2(ab œ acœ bcram somaküee
n bitayÚlzr,
(a œ b)2n = (b œ a)2n
(a œ b)2n œ 1= œ (b œ a)2n œ 1dr
i., (a + b)2 = (a œ b)2 + 4ab
il
5. (a± b)nnnAçÚmÚÚ

PascalÜçgeni
lÚ(a + b)n açÚÚreea nÚlakazan,b
ÚmÚyaplkn,öncn n . kuvvet
en baİayaral
n 0dan baİayartuvtein çpmlÚÚptpanÚ.

lnilakaran kvelrniarÚaryazÚolrSnrn PasalçendkkİÚÚlnarslllni.
lr
oa n nikügnieiarÚ.buuakkatayÚarbeierkÚakbimdeyaplfuvteiein
iÚrakb nii(a œ b)n yuardiçÚancn;çtkvelrndetrmiönüne(+),euvteiein önüne(œ) iartknuu.
tkkvelrndetrmiİeiolr(a + b)3= a3 + 3a2b + 3ab2 + b3
(a œ b)3 = a3 œ 3a2b + 3ab2 œ b3
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 +b4
(a œ b)4 = a4 œ 4a3b + 6a2b2 œ 4ab3 + b4

C. ax2 + bx+ c BĞÇĞMĞNDEKĞ ÜÇ TERĞMLĞNĞN ÇARPANLARA AYRILMASI
çn1. a= 1ii,
lzr,b = m + n vec= m . n omaküeex2 + bx + c= (x + m) (x + n) dri.