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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

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BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter A, Problem 23PE
Textbook Problem
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For Problems 21-24, to write the first four terms of the expansion.

( a 2 b ) 13

To determine

To write:

First four terms of the expansion of (a2b)13.

Explanation of Solution

Let x=aandy=2b.

The binomial expansion for (x+y)n is

xn+nxn1y+n(n1)2!.xn2y2+n(n1)(n2)3!xn3y3+........+yn

The exponents of x begin with the exponent of 13 and decrease term by term by 1 until the last term becomes 1, i.e. the exponent of x is 0.

The exponents of y begin with 0 and increase term by term by 1 until the last term contains the power of 13.

But, here we need to write only first four terms of the expansion.

Therefore,

(a2b)13=a13+13a12(2b)+13122!a11(2b)2+1312113!a10(2b)3

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