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Chapter 12: Q. 317 (page 1221)

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial : y4 term of(y+3)6.

Short Answer

Expert verified

The coefficient ofy4term is135.

Step by step solution

01

Step 1. Given

A binomial is given as (y+3)6.

To find the coefficient of the termy4in the expansion of the given binomial.

02

Step 2. Compare binomial (a+b)n and (y+3)6.

On comparing we get

a=yb=3

and

n=6

Now using binomial expansion,

we have

6-r=4r=2

03

Step 3. Substitute the given values in the formula Crnan-rbr.

We have

C26y6-232=6!鈥�(6-2)!鈥�2!鈥�y4(9)=6!鈥�4!鈥�2!鈥�(9)y4=135y4

The coefficient of the termy4is135.

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