Question

Explain Binomial theorem for positive integral index

Answer 1

$\huge \bf{binomial \: theorem \: for \: positive \: integral}$

➡️The binomial theorem explains the way of expressing and evaluating the powers of a binomial.

➡️ This theorem explains that a term of the form (a+b)n can be expanded and expressed in the form of rasbt, where the exponents s and t are non-negative integers satisfying the condition s + t = n. The coefficient r is a positive integer.

➡️The terms involved are called binomial coefficients and since it is for positive indices it expands only the positive powers.

The general binomial expansion for any index is given by-

(x+y)n = nC0xny0 + nC1x(n-1)y1 + nC2x(n-2)y2 + …….. + nC(n-1) x1y(n-1) + nCnx0yn.