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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 8PE
Textbook Problem
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For Problems 7-20, expand and simplify.

Chapter A, Problem 8PE, For Problems 7-20, expand and simplify.

To determine

To expand:

(x+y)9.

Explanation of Solution

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 9 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 9.

Therefore,

(x+y)9=x9+9x8y+982!x7y2+9873!x6y3+98764!x5y4+987655!x4y5+9876546!x3y6+98765437!x2y7+987654328!xy8

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