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Find the coefficient of the term in x^9 in the expansion of (x+3)^11

 Sep 13, 2020
 #1
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Expand   (x + 3)^11 =

 

x^11 + 33 x^10 + 495 x^9 + 4455 x^8 + 26730 x^7 + 112266 x^6 + 336798 x^5 + 721710 x^4 + 1082565 x^3 + 1082565 x^2 + 649539 x + 177147

 Sep 13, 2020
 #2
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By the binomial theorem, this term is \(\binom{11}{2}x^93^2=55*9x^9=495x^9\rightarrow\boxed{495}\)

 Sep 13, 2020

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