( x + y ) n = ∑ k = 0 n ( n k ) x n − k y k = ∑ k = 0 n ( n k ) x k y n − k (x+y)^n = \sum_{k=0}^n {n \choose k}x^{n-k}y^k = \sum_{k=0}^n {n \choose k}x^{k}y^{n-k}