*The expansion of a binomial for any positive integer n is given by Binomial Theorem, which is (a + b)*^{n}

*= *^{n}C_{0}a^{n} + ^{n}C_{1}a^{n – 1} b + ^{n}C_{2}a^{n – 2} b^{2} + … + ^{n}C_{n – 1 }ab^{n – 1} + ^{n}C_{n}b^{n}

*The coefficients of the expansions are arranged in an array. This array is called Pascal’s triangle.*

*The general term of an expansion (a + b)*^{n} is T_{r + 1} = ^{n}C_{r}a^{n – r}. b^{r}

*In the expansion (a + b)*^{n} , if n is even, then the middle term is the \( \left ( \frac{n}{2} + 1 \right )^\text{th} \) term. If n is odd, then the middle terms are \( \frac{n + 1}{2} \) and \( \left ( \frac{n + 1}{2} +1 \right ) \) terms.