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Chapter 12: Q. 318 (page 1221)

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial :x5term of(x-2)8.

Short Answer

Expert verified

The coefficient ofx5term in the expansion of(x-2)8is-448.

Step by step solution

01

Step 1. Given

A binomial is given as (x-2)8.

To find the coefficient of the termx5in the expansion of the given binomial.

02

Step 2. Compare binomial (a+b)n and (x-2)8.

On Comparing, we get

a=xb=-2n=8

Now in the formula Crnan-rbr,

n-r=58-r=5r=3

03

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

This gives


C38y8-3(-2)3=8!鈥�(8-3)!鈥�3!鈥�y5(-2)3 =-8y58!鈥�5!鈥�3!鈥�=-8y5(56)=-448y5

The coefficient ofy5for(y-2)8is-448.

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