### Intermediate Algebra

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

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter A, Problem 20PE
Textbook Problem
1 views

## For Problems 7-20, expand and simplify. ( x − 1 ) 9

To determine

To expand:

(x1)9.

### Explanation of Solution

Let y=1.

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,

(x1)9=x9+9x8(1)+982!x7(1)2+9873!x6(1)3+98764!x5(1)4+987655!x4(1)5+9876546!x3(1)6+98765437!x2(1)7+987654328!x(1)8+(1)9

Here,

2!=213!=3214!=43215!=543216!=6543217!=7654321

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