Question

Plzz help me to find coefficient in binomial theorem (25 points)

Answer 1

Denote x2 by y.

 

(x2-3)7=(y-3)7

 

This is a binomial expansion in y, and you want the coefficient of y4 because y4=x8

 

You have 7 terms of (y-3) in (y-3)7.  To get the fourth power of y, you need to choose y from four of the terms.  The number of ways you can do this is the combinations of 7 things taken 4 at a time.  This is:

 

7!/(4!3!)=35

So, the coefficient of x8 in the given expansion will be 210.

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