Question

the coefficient of x⁵ is ____ in the expan sion of (x+3)⁸​

Answer 1

It is known that (r+1)th term (Tr+1) in the binomial expansion of

(a+b)n is given by Tr+1=nCraa−rbr

Assuming that x5 occurs in the (r+1)th term of expansion (x+3)8 we obtain 

 Tr+1=8Cr(x)8−r(3)r

Comparing the indices of x in x5 and in Tr+1, we obtain r=3

Thus, the coefficient of x5 is

8C3(3)3=3!5!8!x33=3.2.5!8.7.6.5!.33=1512

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Answer 2

Answer:

The coefficient of x5 is x

and the expansion of(x+3) to the power of 8 is

x+3*3*3*3*3*3*3*3