# What is the link between binomial expansions and Pascal's Triangle?

Oct 19, 2014

Pascal's triangle gives the binomial coefficients.

Pascal's Triangle

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
...

Binomial Coefficients

$\left(\begin{matrix}0 \\ 0\end{matrix}\right)$

$\left(\begin{matrix}1 \\ 0\end{matrix}\right)$ $\left(\begin{matrix}1 \\ 1\end{matrix}\right)$

$\left(\begin{matrix}2 \\ 0\end{matrix}\right)$ $\left(\begin{matrix}2 \\ 1\end{matrix}\right)$ $\left(\begin{matrix}2 \\ 2\end{matrix}\right)$

$\left(\begin{matrix}3 \\ 0\end{matrix}\right)$ $\left(\begin{matrix}3 \\ 1\end{matrix}\right)$ $\left(\begin{matrix}3 \\ 2\end{matrix}\right)$ $\left(\begin{matrix}3 \\ 3\end{matrix}\right)$

$\left(\begin{matrix}4 \\ 0\end{matrix}\right)$ $\left(\begin{matrix}4 \\ 1\end{matrix}\right)$ $\left(\begin{matrix}4 \\ 2\end{matrix}\right)$ $\left(\begin{matrix}4 \\ 3\end{matrix}\right)$ $\left(\begin{matrix}4 \\ 4\end{matrix}\right)$
...

I hope that this was helpful.