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Chapter 12: Q36. (page 637)

Find the indicated term of each expansion.

Fifth term of 2a-b7

Short Answer

Expert verified

The fifth term of the expansion isT5=280a3b4.

Step by step solution

01

Step 1. Given Information.

Given, binomial expansion is 2a-b7 and the fifth term of the expansion is to be determined.

02

Step 2. Calculation.

The general term of the binomial expansion x+yn is given by:

Tr+1=n!n-r!r!xn-ryr

Here n=7, x = 2a, y = -b and r + 1 = 5.

Plugging the values:

Tr+1=n!n鈭�r!r!xn鈭�ryrT5=7!7鈭�4!4!2a7鈭�4鈭�b4T5=7!3!4!2a3b4T5=280a3b4

03

Step 3. Conclusion.

Hence, the third term of the expansion is T5=280a3b4.

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