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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 30PE
Textbook Problem
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For Problems 25-30, find the indicated term of the expansion.

Sixth term of ( 3 a + b ) 7

To determine

To Find:

The sixth term of the expansion (3a+b)7.

Explanation of Solution

Let x=3aandy=b.

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 7 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 7.

But, here we need to find the sixth term of the expansion.

The third term will contain x and y6

Because the sum of the exponents of xandy must be 7

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