Binom yoyilmasi

Binom — ikki hadli ifoda $(a + b)$. Uni $n$-darajaga ko'tarishda koeffitsientlar binom koeffitsientlari $C_n^k$ bo'ladi:

$(a + b)^n = C_n^0 a^n + C_n^1 a^{n-1}b + C_n^2 a^{n-2}b^2 + \dots + C_n^n b^n$

Bu yerda $C_n^k = \dfrac{n!}{k!\,(n - k)!}$. $a$ ning darajasi kamayib, $b$ niki ortib boradi; har bir hadda darajalar yig'indisi $n$.