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In the expansion of  \((ab+bc+ca)^{12}\) find the coefficient of \({a}^{9}{b}^{11}c^{4}\)

 Mar 11, 2019
 #1
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Hey, forgive me for asking but are you a K12 student?

 Mar 11, 2019
 #2
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wdym?

 Mar 11, 2019
 #3
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I'm asking because I am, and I've seen this problem or a binomial theorem problem similar to this before since Im in Honors Alg 2 :) So I'm just wondering if you are.

Guest Mar 11, 2019
edited by Guest  Mar 11, 2019
 #5
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Oh I'm in fifth grade so lol

Guest Mar 11, 2019
 #6
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Oh ok lol

Guest Mar 11, 2019
 #4
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We can write this as

 

[ b(a + c) + ca ] 12

 

We have .....

 

C( 12, 1) * [ b ( a + c)]11 * (ca)1   =

 

(12)b11 * (a + c)11 * a1 c1  =

 

(12)acb11 * (a + c)11  =

 

(12)acb11 *  C(11,3) (a)8 * c3  =

 

(12) acb11 * (165)a8 c3  =

 

1980  a9 b11  c4

 

 

cool cool cool

 Mar 11, 2019

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