Find the coefficient of

(i)x5 in the expansion of (x + 3)8


(ii) x6 in the expansion of .


(iii) x-15 in the expansion of .


(iv) a7b5 in the expansion of (a – 2b)12.


(i) Here, a=x, b=3 and n=8


We have a formula,





To get coefficient of x5 we must have,


(x)8-r = x5


• 8 - r = 5


• r = 3


Therefore, coefficient of x5



= 1512


(ii) Here, a=3x2, and n=9


We have a formula,








To get coefficient of x6 we must have,


(x)18-3r = x6


• 18 - 3r = 6


• 3r = 12


• r = 4


Therefore, coefficient of x6



= 126×3


= 378


(iii) Here, a=3x2, and n=10


We have a formula,








To get coefficient of x-15 we must have,


(x)20-5r = x-15


• 20 - 5r = -15


• 5r = 35


• r = 7


Therefore, coefficient of x-15


But ……….


Therefore, qthe coefficient of x-15





(iv) Here, a=a, b=-2b and n=12


We have formula,





To get coefficient of a7b5 we must have,


(a)12-r (b)r = a7b5


• r = 5


Therefore, coefficient of a7b5



= 792. (-32)


= -25344


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