Binomial Polinom Formula

Binomial Polinom Formula Welcome to my blog,,
The following is a power formula of the form $\displaystyle (x+y)^n$:
$\displaystyle (x+y)^n=\sum_{k=0}^n C_k^n x^{n-k} y^k$
where $\displaystyle C_k^n = \frac{n!}{k!.(n-k)!}$

The coefficients of the polynomial terms formed into Pascal's triangular number pattern.
Consider the following example:
We know Pascal's triangular numbers, for example we write up to level 4,
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
We can see the coefficient of level 4(bottom one) which is 1 4 6 4 1 will result from the combination of $C_k^n$ with $n=4$ and $k=0,~1,~2,~3, ~4$.
So we are sure that
$\displaystyle (x+y)^4=x^4+4x^3y+6x^2y^2+4xy^3+y^4$.
Thanks, and happy learning.