The expansion of a binomial for any positive integral n is given by Binomial Theorem, which is (a + b)ⁿ = ⁿC₀aⁿ + ⁿC₁a^n-1b + ⁿC₂a^n-2b² + ...+ ⁿC_n-1a.b^n-1 + ⁿC_nbⁿ.

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 = ⁿC_ra^n-rb^r. In the expansion (a + b)ⁿ, if n is even, then the middle term is the (n/2 + 1)th term. If n is odd, then the middle terms are (n + 1)/2 th and [(n + 1)/2 + 1] th terms.