Формулы сокращённого умножения

\[ (a + b)^2 = a^2 + 2ab + b^2 \] \[ (a - b)^2 = a^2 - 2ab + b^2 \] \[ a^2 - b^2 = (a - b)(a + b) \] \[ (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc \]

\[ (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \] \[ (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \] \[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \] \[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]

\[ (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 \] \[ (a - b)^4 = a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4 \] \[ a^4 - b^4 = (a - b)(a + b)(a^2 + b^2) \]

\[ (a + b)^n = a^n + na^{n-1}b + \frac{n(n - 1)}{2}a^{n-2}b^2 + \ldots + \frac{n!}{k!(n - k)!}a^{n - k}b^k + \ldots + b^n \] \[ (a - b)^n = a^n - na^{n-1}b + \frac{n(n - 1)}{2}a^{n-2}b^2 - \ldots + (-1)^k \frac{n!}{k!(n - k)!}a^{n - k}b^k + \ldots + (-1)^n b^n \]