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Chapter 12: Q. 319 (page 1221)

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial :a3b4term of(2a+b)7.

Short Answer

Expert verified

The coefficient of a3b4term in the expansion of (2a+b)7 is280.

Step by step solution

01

Step 1. Given 

A binomial is given as (2a+b)7.

To find the coefficient of the term a3b4in the expansion of the given binomial.

02

Step 2. Compare binomial (a+b)n and  (2a+b)7.

On Comparing, we get

a=2ab=bn=7

Now in the formula ,

n-r=37-r=3r=4

03

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

We get

C47(2a)7-4b4=7!鈥�(7-4)!鈥�4!鈥�(8a3)b4=35(8a3)b4=280a3b4

The coefficient of the terma3b4for the given binomial is280.

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