Binomial Expression
An expression consisting of two terms, connected by + or – sign is called binomial expression.

Binomial Theorem
If a and b are real numbers and n is a positive integer, then

The general term of (r + 1)^th term in the expression is given by
T_r+1 = ⁿC_r a^n-r b^r

Some Important

General and Middle Terms

• Binomial Theorem: The expansion of a binomial for any positive integral n is given by Binomial Theorem, which is
  
• The coefficients of the expansions are arranged in an array. This array is called Pascal’s triangle.
• The general term of an expansion 
• The general term of an expansion 
• The general term of 
• The general term of 
• In the expansion , if n is even, then the middle term is the  term. If n is odd, then the middle terms are and  terms.
•  term from the end in  term fromt he beginning.
• Method to prove Binomial Theorem:

(a) Principle of Mathematical Induction.

(b) Combinatorial Method.

• Factorial notation:
  (i)  
  (ii) 
  (iii) 
  (iv)