Q8.1Long answer
Overview: 8.1.1 An expression consisting of two terms, connected by + or – sign is called a 1 1 4 binomial expression. For example, x + a, 2x – 3y, − 3 , 7x − , etc., are all binomial x x 5y expressions. 8.1.2 Binomial theorem If a and b are real numbers and n is a positive integer, then (a + b)n =nC0 an + nC1 an – 1 b1 + nC2 an – 2 b2 + ... ... + nCr an – r br + ... + nCn bn, where nCr = for 0 ≤ r ≤ n r n−r The general term or (r + 1)th term in the expansion is given by Tr + 1 = nCr an–r br 8.1.3 Some important observations 1. The total number of terms in the binomial expansion of (a + b)n is n + 1, i.e. one more than the exponent n.