Page 38 - Math SL HB Sem 1
P. 38
BNO\{1.{L THFr)RE},4
n nl
\ote: C6 1
) - 01!
L) 0!(n
nl nx(n-l)t
Cr
t;) 1!(n-l)! l!(n-1)!
nl n x (n I) x (n 2)l * n x (n - 1)
-
-
2l(n - 2)r. 2!x (n 2)l )l
-
("\ nl nx x (n
l^ l= e : ln -1) -2)(n -3)l _ nx(n- 1)(n- 2)
3l(ru 3)! 3!x (n 3)! lr
-
BINOMIAL EXPANSION
\
7
r^rivrirl.il (ir€zrir), t,{u lcr,ii ina fonn uf (x ry) is rarsed to apo\ver orn - Dutumnt
expansion
Consider ( x - l') n. we will get the expansion as below.:
:
n 0, i
n:1; x + v
n:2. X. + 2xy l v )
n:l; xr 1 3x2Y + 3 *y? + yl
n=4; xo * 4xjy s 6*,\, + 4 xyj + y,{
and so forth. The pattem will continue till the desired n . The process is boring and long.
Therefore a technique called. Binomial Theorem is being introduced.
Binomial Theorem
Definilion:
( t7 ln\
(\ r\') - ,.' . x y+ +l lx
[;) l. l,.j
n
+--.+ x)/ n- l +
n-l )'
: r" + x,'r y . n(n-l\ r2
1n)
2!
I n rn'r,'.rr'lrereneZ*
