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 7PE
Textbook Problem
20 views

For Problems 7-20, expand and simplify. ( x + y ) 10

To determine

To expand:

(x+y)10.

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 10 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 10.

Therefore,

(x+y)10=x10+10x9y+1092!x8y2+10983!x7y3+109874!x6y4+1098765!x5y5+10987656!x4y6+109876547!x3y7+1098765438!x2y8+10987654329!xy9+y10

Here,

2!=213!=3214!=43215!=543216!=6543217!=76543218!=876543219!=987654321

Therefore,

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