nightweaver066
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Re: HSC 2013 3U Marathon Thread
![](https://latex.codecogs.com/png.latex?\bg_white (1+x)^{n^2} = \binom{n^2}{0} + {n^2}{1}x + ... +\binom{n^2}{n^2}x^{n^2} ... (1))
![](https://latex.codecogs.com/png.latex?\bg_white [(1 + x)^n]^n)
![](https://latex.codecogs.com/png.latex?\bg_white = [\binom{n}{0} + \binom{n}{1}x + \binom{n}{2}x^2 + ... + \binom{n}{n}x^n]^n ... (2))
![](https://latex.codecogs.com/png.latex?\bg_white $Coefficient of $ x^2 $ in $ (1) = \binom{n^2}{2})
![](https://latex.codecogs.com/png.latex?\bg_white $Coefficient of $ x^2 $ in $ (2) = \binom{n}{0}^{n-1} \binom{n}{2} \times \binom{n}{n-1} $ (Selecting the n-1 brackets, then 1 remaining for the $ x^2 $)$)
![](https://latex.codecogs.com/png.latex?\bg_white + \binom{n}{0}^{n-2} \binom{n}{1}^2 \times \binom{n}{n-2} $ (Selecting the n-2 brackets, then 2 remaining for the x)$)
![](https://latex.codecogs.com/png.latex?\bg_white = \binom{n}{1} \binom{n}{2} + \binom{n}{1}^2 \binom{n}{2} $ As $ \binom{n}{r} = \binom{n}{n-r})
![](https://latex.codecogs.com/png.latex?\bg_white = \binom{n}{1} \binom{n}{2} [1 + \binom{n}{1}])
can u please reveal the solution to this question?![]()