Binomial TheoremDate: 8/5/96 at 17:12:22 From: Anonymous Subject: Binomial Theorem Find the fourth term of (2a - 6b)^11 I got (11) 3 however I am not quite sure how to approach the problem afterwards. Your help would be greatly appreciated. Thanks! Date: 8/5/96 at 17:46:48 From: Doctor Paul Subject: Re: Binomial Theorem You have to begin by writing out Pascal's Triangle (from the Binomial Theorem): 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1 1 11 55 165 330 462 462 330 165 55 11 1 1*(2a)^11 + 11*[(2a)^10 * (-6b)^1] + 55*[(2a)^9 * (-6b)^2] + 165*[(2a)^8 * (-6b)^3] ^^^^^^^^^^^^^^^^^^^^^^ so there's your fourth term. I suppose you could multiply it out if you wanted to: 165*[256*a^8 * -216*b^3] 165 * [ -55296 a^8 b^3] -9123840 * a^8 * b^3 -Doctor Paul, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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