Binomial Theorem

Let Us Learn What Is Binomial.


The sum of two monomial is called Binomial.

Binomial Theorem for Positive Integral Indices

Let us have a look at the following identities done earlier:

(a+ b)0 = 1 a + b ≠ 0
(a+ b)1 = a + b
(a+ b)2 = a2 + 2ab + b2
(a+ b)3 = a3 + 3a2b + 3ab2 + b3
(a+ b)4 = (a + b)3 (a + b) = a4 + 4a3b + 6a2b2 + 4ab3 + b4

In these expansions, we observe that

(i) The total number of terms in the expansion is one more than the index. For
example, in the expansion of (a + b)2 , number of terms is 3 whereas the index of
(a + b)2 is 2.

(ii) Powers of the first quantity ‘a’ go on decreasing by 1 whereas the powers of the
second quantity ‘b’ increase by 1, in the successive terms.

(iii) In each term of the expansion, the sum of the indices of a and b is the same and
is equal to the index of a + b.

Examples Using Binomial Theorem