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Coefficient of x^3by Stacyg
Tags: coefficient 
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#1
May1508, 06:06 PM

P: 25

Find the coefficient of x^3 in the expansion of (2x^23/x)^3
I know how to do simple coefficients using pascalles triangle but I really don't know how to do this. Any help would be much appreciated. 


#2
May1508, 06:08 PM

P: 738

Write it as
[tex](2x^2  3x^{1})^3[/tex] From Pascal's triangle, you know how to expand [tex](a+b)^n[/tex] What can you replace with a and what can you replace with b? 


#3
May1508, 06:09 PM

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[tex](2x^2\frac{3}{x})^3[/tex]
[tex] (\frac{1}{x}(2x^33))^3[/tex] How about now? 


#4
May1508, 06:10 PM

P: 738

Coefficient of x^3
Oh, that's a nice way of doing it :)



#5
May1508, 07:36 PM

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P: 6,202

as for [itex](a+b)^n[/itex] is valid for [itex]\frac{b}{a}<1[/itex] But if a and b are variables, you'll have to do some fancy algebra to get the range for which it is valid. 


#6
May1508, 08:23 PM

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#7
May1508, 08:53 PM

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That's what I was taught.."validity of a binomial"



#8
May1508, 10:30 PM

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#9
May1508, 10:37 PM

P: 63

Besides, we're dealing with polynomials in the case of (a+b)^n



#10
May1508, 10:46 PM

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