Page 149 - Fixtures

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n yx

(x + y)n = C (n, 0)x n + C (n,1)x n−1y + C (n, 2)x n−2y2

+ + C(n,n − 1)xyn−1 + C (n,n)yn

(x + y)n :

xn−jy j M j = 0,1,2,…,n Mxn−jy j
j xn−jy j
M ) M.
,
nx n−j
y
.(

n n−j

.C(n,n − j) = C(n, j)

.(3x − 2)6 ()

(3x − 2)6 = C(6, 0)(3x)6 + C (6,1)(3x)5(−2)1 + C (6, 2)(3x)4(−2)2
+ C (6, 3)(3x)3(−2)3 + C (6, 4)(3x)2(−2)4
+ C (6, 5)(3x)1(−2)5 + C (6, 6)(−2)6

= 729x 6 − 2916x 5 + 4860x 4 − 4320x 3
+ 2160x 2 − 576x + 64

(x + 2x2)2(1 − 2x)5 x3 ( )