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?

OfficialBubbleTanks
Dec 4, 2017

#1**+1 **

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.

Melody
Dec 4, 2017