Holt Mcdougal Larson Algebra 2: Student Edition 2012
Holt Mcdougal Larson Algebra 2: Student Edition 2012
1st Edition
ISBN: 9780547647159
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
Expert Solution & Answer
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Chapter 6.2, Problem 6Q
Solution

To write: the binomial expansion using the binomial theorem.

  2s36=64s6576s5+2160s44320s3+4860s22916s+729

Given information:

The given expression is:

  2s36

Formula Used:

Combinations of n Objects Taken r at a Time

The number of combinations of r objects taken from a group of n distinct objects is denoted by Cnr and is given by the formula:

  Cnr=n!nr!r! .

  Cn0=1Cnn=1

Theorem Used:

Binomial Theorem

For any positive integer n , the binomial expansion of a+bn is:

  a+bn=Cn0anb0+Cn1an1b1+Cn2an2b2++Cnna0bn

Here, each term in the expansion of a+bn has the form Cnranrbr where r s an integer from 0 to n .

Explanation:

By using the binomial theorem, the given expression 2s36 is written in expanded form as:

   2s3 6 = 2s+ 3 6

   = C 6 0 2s 6 3 0 + C 6 1 2s 5 3 1 + C 6 2 2s 4 3 2 + C 6 3 2s 3 3 3 + C 6 4 2s 2 3 4 + C 6 5 2s 1 3 5 + C 6 6 2s 0 3 6

   = 6! 60 !0! 64 s 6 1 + 6! 61 !1! 32 s 5 3 + 6! 62 !2! 16 s 4 9 + 6! 63 !3! 8 s 3 27 + 6! 64 !4! 4 s 2 81 + 6! 65 !5! 2 s 1 243

   + 6! 66 !6! 1 729 =1 64 s 6 1 + 6 32 s 5 3 + 15 16 s 4 9 + 20 8 s 3 27 + 15 4 s 2 81 + 6 2 s 1 243 + 1 1 729 =64 s 6 576 s 5 +2160 s 4 4320 s 3 +4860 s 2 2916s+729

Chapter 6 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 6.1 - Prob. 11GPCh. 6.1 - Prob. 12GPCh. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.1 - Prob. 8ECh. 6.1 - Prob. 9ECh. 6.1 - Prob. 10ECh. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48PSCh. 6.1 - Prob. 49PSCh. 6.1 - Prob. 50PSCh. 6.1 - Prob. 51PSCh. 6.1 - Prob. 53PSCh. 6.2 - Prob. 1GPCh. 6.2 - Prob. 2GPCh. 6.2 - Prob. 3GPCh. 6.2 - Prob. 4GPCh. 6.2 - Prob. 5GPCh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 43PSCh. 6.2 - Prob. 44PSCh. 6.2 - Prob. 45PSCh. 6.2 - Prob. 46PSCh. 6.2 - Prob. 47PSCh. 6.2 - Prob. 48PSCh. 6.2 - Prob. 49PSCh. 6.2 - Prob. 1QCh. 6.2 - Prob. 2QCh. 6.2 - Prob. 3QCh. 6.2 - Prob. 4QCh. 6.2 - Prob. 5QCh. 6.2 - Prob. 6QCh. 6.2 - Prob. 7QCh. 6.2 - Prob. 8QCh. 6.2 - Prob. 9QCh. 6.2 - Prob. 10QCh. 6.2 - Prob. 11QCh. 6.2 - Prob. 12QCh. 6.2 - Prob. 13QCh. 6.2 - Prob. 14QCh. 6.2 - Prob. 15QCh. 6.2 - Prob. 16QCh. 6.2 - Prob. 17QCh. 6.2 - Prob. 1PCh. 6.2 - Prob. 2PCh. 6.2 - Prob. 3PCh. 6.2 - Prob. 4PCh. 6.2 - Prob. 1MRPSCh. 6.2 - Prob. 2MRPSCh. 6.2 - Prob. 3MRPSCh. 6.2 - Prob. 4MRPSCh. 6.2 - Prob. 5MRPSCh. 6.2 - Prob. 6MRPSCh. 6.2 - Prob. 7MRPSCh. 6.2 - Prob. 8MRPSCh. 6.2 - Prob. 1DCCh. 6.3 - Prob. 1GPCh. 6.3 - Prob. 2GPCh. 6.3 - Prob. 3GPCh. 6.3 - Prob. 4GPCh. 6.3 - Prob. 5GPCh. 6.3 - Prob. 6GPCh. 6.3 - Prob. 7GPCh. 6.3 - Prob. 8GPCh. 6.3 - Prob. 9GPCh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - Prob. 26ECh. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - Prob. 30ECh. 6.3 - Prob. 31PSCh. 6.3 - Prob. 32PSCh. 6.3 - Prob. 33PSCh. 6.3 - Prob. 34PSCh. 6.3 - Prob. 35PSCh. 6.3 - Prob. 36PSCh. 6.3 - Prob. 1PCh. 6.3 - Prob. 2PCh. 6.4 - Prob. 1GPCh. 6.4 - Prob. 2GPCh. 6.4 - Prob. 3GPCh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27PSCh. 6.4 - Prob. 28PSCh. 6.4 - Prob. 29PSCh. 6.4 - Prob. 30PSCh. 6.4 - Prob. 31PSCh. 6.4 - Prob. 32PSCh. 6.4 - Prob. 1DCCh. 6.4 - Prob. 2DCCh. 6.5 - Prob. 1GPCh. 6.5 - Prob. 2GPCh. 6.5 - Prob. 3GPCh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13PSCh. 6.5 - Prob. 14PSCh. 6.5 - Prob. 15PSCh. 6.5 - Prob. 17PSCh. 6.5 - Prob. 18PSCh. 6.5 - Prob. 1QCh. 6.5 - Prob. 2QCh. 6.5 - Prob. 3QCh. 6.5 - Prob. 4QCh. 6.5 - Prob. 5QCh. 6.5 - Prob. 6QCh. 6.5 - Prob. 7QCh. 6.5 - Prob. 8QCh. 6.5 - Prob. 1DCCh. 6.5 - Prob. 2DCCh. 6.5 - Prob. 3DCCh. 6.5 - Prob. 1MRPSCh. 6.5 - Prob. 2MRPSCh. 6.5 - Prob. 3MRPSCh. 6.5 - Prob. 4MRPSCh. 6.5 - Prob. 5MRPSCh. 6.5 - Prob. 6MRPSCh. 6.5 - Prob. 7MRPSCh. 6.5 - Prob. 8MRPSCh. 6 - Prob. 1VECh. 6 - Prob. 2VECh. 6 - Prob. 3VECh. 6 - Prob. 1REAECh. 6 - Prob. 2REAECh. 6 - Prob. 3REAECh. 6 - Prob. 4REAECh. 6 - Prob. 5REAECh. 6 - Prob. 6REAECh. 6 - Prob. 7REAECh. 6 - Prob. 8REAECh. 6 - Prob. 9REAECh. 6 - Prob. 10REAECh. 6 - Prob. 11REAECh. 6 - Prob. 12REAECh. 6 - Prob. 13REAECh. 6 - Prob. 14REAECh. 6 - Prob. 15REAECh. 6 - Prob. 16REAECh. 6 - Prob. 17REAECh. 6 - Prob. 18REAECh. 6 - Prob. 19REAECh. 6 - Prob. 20REAECh. 6 - Prob. 21REAECh. 6 - Prob. 22REAECh. 6 - Prob. 23REAECh. 6 - Prob. 24REAECh. 6 - Prob. 1TCh. 6 - Prob. 2TCh. 6 - Prob. 3TCh. 6 - Prob. 4TCh. 6 - Prob. 5TCh. 6 - Prob. 6TCh. 6 - Prob. 7TCh. 6 - Prob. 8TCh. 6 - Prob. 9TCh. 6 - Prob. 10TCh. 6 - Prob. 11TCh. 6 - Prob. 12TCh. 6 - Prob. 13TCh. 6 - Prob. 14TCh. 6 - Prob. 15TCh. 6 - Prob. 16TCh. 6 - Prob. 17TCh. 6 - Prob. 18TCh. 6 - Prob. 19TCh. 6 - Prob. 20TCh. 6 - Prob. 21TCh. 6 - Prob. 22TCh. 6 - Prob. 23TCh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 1TPCh. 6 - Prob. 2TPCh. 6 - Prob. 3TPCh. 6 - Prob. 4TPCh. 6 - Prob. 5TPCh. 6 - Prob. 6TPCh. 6 - Prob. 7TPCh. 6 - Prob. 8TPCh. 6 - Prob. 9TPCh. 6 - Prob. 10TPCh. 6 - Prob. 11TPCh. 6 - Prob. 12TPCh. 6 - Prob. 13TPCh. 6 - Prob. 14TPCh. 6 - Prob. 15TPCh. 6 - Prob. 16TPCh. 6 - Prob. 17TPCh. 6 - Prob. 18TPCh. 6 - Prob. 19TP
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