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so i dont know the difference between the binomial theorem and pascals triangle. why do they give such different solutions. 

 

one example. 

(2x-3)^4 can give two very different (and long) solutions

why?

 Dec 4, 2017
 #1
avatar+100168 
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They don't they are the same.

 

(2x-3)^4

 

The 4 line of pascals triangle is  14641

so

 

\((2x-3)^4\\=1*(2x)^4+4*(2x)^3*(-3)^1+6*(2x)^2*(-3)^2+4*(2x)^1*(-3)^3+1*(-3)^4\\ =1*16x^4+4*8x^3*-3+6*4x^2*9+4*2x^1*-27+1*81\\~\\ =1*16x^4+4*-24x^3\;\;+\;\;6*36x^2\;\;+\;\;4*-54x\;\;+\;\;1*81\\~\\ =16x^4-96x^3+216x^2-216x+81 \)

 

 

There could be careless errors but this should be the same as if you expand it in any other way.

 Dec 4, 2017
 #2
avatar+100168 
0

Here is Wolfram alpha's answer. I think it is the same:

http://www.wolframalpha.com/input/?i=expand+(2x-3)%5E4

Melody  Dec 4, 2017

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