Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 11.6, Problem 2CYP
To determine

The expansion of the binomial (x+y)10

Expert Solution & Answer
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Answer to Problem 2CYP

The expand form is:

  x10+10x9y+45x8y2+120x7y3+210x6y4+252x5y5+210x4y6+120x3y7+45x2y8+10xy9+y10

Explanation of Solution

Given information:

The given expression is as:

  (x+y)10

Concept used:

  1. The binomial expansion for (x+y)n is as:

  (x+y)n=r=0n(nr)xnryr

Where the coefficient for term xnryr is (nr)=n!r!(nr)!

Calculation:

Since, the given expression is as:

  (x+y)10

On comparing this with (x+y)n , the value of n is 10

  n=10

On employing binomial expansion, we can express given expression as

  (x+y)10=r=010(10r)x10ryr

Therefore, the expand for (x+y)10 is

   ( x+y ) 10 = r=0 10 ( 10 r ) x 10r y r

   = 10! ( 100 )!0! ( x ) 100 ( y ) 0 + 10! ( 101 )!1! ( x ) 101 ( y ) 1 + 10! ( 102 )!2! ( x ) 102 ( y ) 2

   + 10! ( 103 )!3! ( x ) 103 ( y ) 3 + 10! ( 104 )!4! ( x ) 104 ( y ) 4 + 10! ( 105 )!5! ( x ) 105 ( y ) 5

   + 10! ( 106 )!6! ( x ) 106 ( y ) 6 + 10! ( 103 )!7! ( x ) 103 ( y ) 3 + 10! ( 108 )!8! ( x ) 108 ( y ) 8

   + 10! ( 109 )!9! ( x ) 109 ( y ) 9 + 10! ( 1010 )!10! ( x ) 1010 ( y ) 10

   = x 10 +10 x 9 y+45 x 8 y 2 +120 x 7 y 3 +210 x 6 y 4 +252 x 5 y 5 +210 x 4 y 6 +120 x 3 y 7 +45 x 2 y 8 +10x y 9 + y 10

Thus, the expansion of the given binomial is,

  x10+10x9y+45x8y2+120x7y3+210x6y4+252x5y5+210x4y6+120x3y7+45x2y8+10xy9+y10

Chapter 11 Solutions

Algebra 2

Ch. 11.1 - Prob. 1CYUCh. 11.1 - Prob. 2CYUCh. 11.1 - Prob. 3CYUCh. 11.1 - Prob. 4CYUCh. 11.1 - Prob. 5CYUCh. 11.1 - Prob. 6CYUCh. 11.1 - Prob. 7CYUCh. 11.1 - Prob. 8CYUCh. 11.1 - Prob. 9CYUCh. 11.1 - Prob. 10CYUCh. 11.1 - Prob. 11CYUCh. 11.1 - Prob. 12CYUCh. 11.1 - Prob. 13CYUCh. 11.1 - Prob. 14CYUCh. 11.1 - Prob. 15CYUCh. 11.1 - Prob. 16CYUCh. 11.1 - Prob. 17CYUCh. 11.1 - Prob. 18CYUCh. 11.1 - Prob. 19CYUCh. 11.1 - Prob. 20CYUCh. 11.1 - Prob. 21PPSCh. 11.1 - Prob. 22PPSCh. 11.1 - Prob. 23PPSCh. 11.1 - Prob. 24PPSCh. 11.1 - Prob. 25PPSCh. 11.1 - Prob. 26PPSCh. 11.1 - Prob. 27PPSCh. 11.1 - Prob. 28PPSCh. 11.1 - Prob. 29PPSCh. 11.1 - Prob. 30PPSCh. 11.1 - Prob. 31PPSCh. 11.1 - Prob. 32PPSCh. 11.1 - Prob. 33PPSCh. 11.1 - Prob. 34PPSCh. 11.1 - Prob. 35PPSCh. 11.1 - Prob. 36PPSCh. 11.1 - Prob. 37PPSCh. 11.1 - Prob. 38PPSCh. 11.1 - Prob. 39PPSCh. 11.1 - Prob. 40PPSCh. 11.1 - Prob. 41PPSCh. 11.1 - Prob. 42PPSCh. 11.1 - Prob. 43PPSCh. 11.1 - Prob. 44PPSCh. 11.1 - Prob. 45PPSCh. 11.1 - Prob. 46PPSCh. 11.1 - 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Prob. 50STPCh. 11.7 - Prob. 51SCh. 11.7 - Prob. 52SCh. 11.7 - Prob. 53SCh. 11.7 - Prob. 54SCh. 11.7 - Prob. 55SCh. 11.7 - Prob. 56SCh. 11.7 - Prob. 57SCh. 11.7 - Prob. 58SCh. 11.7 - Prob. 59SCh. 11.7 - Prob. 60SCh. 11.7 - Prob. 61SCh. 11.7 - Prob. 62SCh. 11 - Prob. 1QCCh. 11 - Prob. 2QCCh. 11 - Prob. 3QCCh. 11 - Prob. 4QCCh. 11 - Prob. 5QCCh. 11 - Prob. 6QCCh. 11 - Prob. 7QCCh. 11 - Prob. 8QCCh. 11 - Prob. 9QCCh. 11 - Prob. 10QCCh. 11 - Prob. 11QCCh. 11 - Prob. 12QCCh. 11 - Prob. 13QCCh. 11 - Prob. 14QCCh. 11 - Prob. 1MCQCh. 11 - Prob. 2MCQCh. 11 - Prob. 3MCQCh. 11 - Prob. 4MCQCh. 11 - Prob. 5MCQCh. 11 - Prob. 6MCQCh. 11 - Prob. 7MCQCh. 11 - Prob. 8MCQCh. 11 - Prob. 9MCQCh. 11 - Prob. 10MCQCh. 11 - Prob. 11MCQCh. 11 - Prob. 12MCQCh. 11 - Prob. 13MCQCh. 11 - Prob. 14MCQCh. 11 - Prob. 15MCQCh. 11 - Prob. 16MCQCh. 11 - Prob. 17MCQCh. 11 - Prob. 18MCQCh. 11 - Prob. 19MCQCh. 11 - Prob. 20MCQCh. 11 - Prob. 1SGRCh. 11 - Prob. 2SGRCh. 11 - Prob. 3SGRCh. 11 - Prob. 4SGRCh. 11 - Prob. 5SGRCh. 11 - Prob. 6SGRCh. 11 - Prob. 7SGRCh. 11 - Prob. 8SGRCh. 11 - Prob. 9SGRCh. 11 - Prob. 10SGRCh. 11 - Prob. 11SGRCh. 11 - Prob. 12SGRCh. 11 - Prob. 13SGRCh. 11 - Prob. 14SGRCh. 11 - Prob. 15SGRCh. 11 - Prob. 16SGRCh. 11 - Prob. 17SGRCh. 11 - Prob. 18SGRCh. 11 - Prob. 19SGRCh. 11 - Prob. 20SGRCh. 11 - Prob. 21SGRCh. 11 - Prob. 22SGRCh. 11 - Prob. 23SGRCh. 11 - Prob. 24SGRCh. 11 - Prob. 25SGRCh. 11 - Prob. 26SGRCh. 11 - Prob. 27SGRCh. 11 - Prob. 28SGRCh. 11 - Prob. 29SGRCh. 11 - Prob. 30SGRCh. 11 - Prob. 31SGRCh. 11 - Prob. 32SGRCh. 11 - Prob. 33SGRCh. 11 - Prob. 34SGRCh. 11 - Prob. 35SGRCh. 11 - Prob. 36SGRCh. 11 - Prob. 37SGRCh. 11 - Prob. 38SGRCh. 11 - Prob. 39SGRCh. 11 - Prob. 40SGRCh. 11 - Prob. 41SGRCh. 11 - Prob. 42SGRCh. 11 - Prob. 43SGRCh. 11 - Prob. 44SGRCh. 11 - Prob. 45SGRCh. 11 - Prob. 46SGRCh. 11 - Prob. 47SGRCh. 11 - Prob. 48SGRCh. 11 - Prob. 49SGRCh. 11 - Prob. 50SGRCh. 11 - Prob. 51SGRCh. 11 - Prob. 52SGRCh. 11 - Prob. 53SGRCh. 11 - Prob. 54SGRCh. 11 - Prob. 55SGRCh. 11 - Prob. 56SGRCh. 11 - Prob. 57SGRCh. 11 - Prob. 58SGRCh. 11 - Prob. 59SGRCh. 11 - Prob. 60SGRCh. 11 - Prob. 61SGRCh. 11 - Prob. 62SGRCh. 11 - Prob. 63SGRCh. 11 - Prob. 64SGRCh. 11 - Prob. 65SGRCh. 11 - Prob. 66SGRCh. 11 - Prob. 67SGRCh. 11 - Prob. 68SGRCh. 11 - Prob. 69SGRCh. 11 - Prob. 1PTCh. 11 - Prob. 2PTCh. 11 - Prob. 3PTCh. 11 - Prob. 4PTCh. 11 - Prob. 5PTCh. 11 - Prob. 6PTCh. 11 - Prob. 7PTCh. 11 - Prob. 8PTCh. 11 - Prob. 9PTCh. 11 - Prob. 10PTCh. 11 - Prob. 11PTCh. 11 - Prob. 12PTCh. 11 - Prob. 13PTCh. 11 - Prob. 14PTCh. 11 - Prob. 15PTCh. 11 - Prob. 16PTCh. 11 - Prob. 17PTCh. 11 - Prob. 18PTCh. 11 - Prob. 19PTCh. 11 - Prob. 20PTCh. 11 - Prob. 21PTCh. 11 - Prob. 22PTCh. 11 - Prob. 23PTCh. 11 - Prob. 24PTCh. 11 - Prob. 1ECh. 11 - Prob. 2ECh. 11 - Prob. 1STPCh. 11 - Prob. 2STPCh. 11 - Prob. 3STPCh. 11 - Prob. 4STPCh. 11 - Prob. 5STPCh. 11 - Prob. 6STPCh. 11 - Prob. 7STPCh. 11 - Prob. 8STPCh. 11 - Prob. 9STPCh. 11 - Prob. 10STPCh. 11 - Prob. 11STPCh. 11 - Prob. 12STPCh. 11 - Prob. 13STPCh. 11 - Prob. 14STPCh. 11 - Prob. 15STPCh. 11 - Prob. 16STPCh. 11 - Prob. 17STPCh. 11 - Prob. 18STP
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