Binomial theorem

bt

\begin{pmatrix} n \\ 0 \end{pmatrix}x^ny^0 + \begin{pmatrix} n \\ 1 \end{pmatrix}x^{n-1}y^1+ \begin{pmatrix} n \\ 2 \end{pmatrix}x^{n-2}y^2+\dots+ \begin{pmatrix} n \\ n-1 \end{pmatrix}x^1y^{n-1}+ \begin{pmatrix} n \\ n \end{pmatrix}x^0y^n

(x+y)^n = \displaystyle\sum_{k=0}^n \begin{pmatrix} n \\ k \end{pmatrix} x^{n-k}y^k = \displaystyle\sum_{k=0}^n \begin{pmatrix} n \\ k \end{pmatrix} x^ky^{n-k} = \begin{pmatrix} n \\ 0 \end{pmatrix}x^ny^0 + \begin{pmatrix} n \\ 1 \end{pmatrix}x^{n-1}y^1+ \begin{pmatrix} n \\ 2 \end{pmatrix}x^{n-2}y^2+\dots+ \begin{pmatrix} n \\ n-1 \end{pmatrix}x^1y^{n-1}+ \begin{pmatrix} n \\ n \end{pmatrix}x^0y^n

or

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