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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 14PE
Textbook Problem
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For Problems 7-20, expand and simplify

( 2 a 3 b ) 4

To determine

To expand:

(2a3b)4.

Explanation of Solution

Let x=2aandy=3b.

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 4 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 4.

Therefore,

(2a3b)4=(2a)4+4(2a)3(3b)+432!(2a)2(3b)2+4323!(2a)(3b)3+(3b)4

Here,

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