Binomial Theorem

(x+y)^{n} = {}^{n}C_{0}x^{n}y^{0} + {}^{n}C_{1}x^{n-1}y^{1} + ... + {}^{n}C_{n-1}x^{1}y^{n-1} + {}^{n}C_{n}x^{0}y^{n} = sum_{r=0}^{n} {}^{n}C_{r}x^{n-

(1+x)^{n} = sum_{r=0}^{n} {}^{n}C_{r}x^{r}

(1-x)^{n} = sum_{r=0}^{n} {}^{n}C_{r}(-1)^{r}x^{r}

2^{n} = {}^{n}C_{0} + {}^{n}C_{1} + ... + {}^{n}C_{n}

T_{r+1} = {}^{n}C_{r}x^{n-r}y^{r}

r^{th} term from end = T_{n-r+2}

Middle term when n is even: ((n+2)/2)^{th} term

Middle terms when n is odd: ((n+1)/2)^{th} term and ((n+3)/2)^{th} term