Binomial Theorem Solutions  Formula, Worksheet, Calculator and Examples.
Binomial Theorem Questions  Page 4
Binomial Theorem Video Lecture  Page 5
However, for higher powers like , etc., the calculations become difficult by using repeated multiplication. This difficulty was overcome by a theorem known as binomial theorem. It gives an easier way to expand , where n is an integer o r a rational number.
Binomial Theorem for Positive Integral Indices
Let us have a look at the following identities done earlier
a + b ≠ 0
In these expansions, we observe that
 The total number of terms in the expansion is one more than the index. For example, in the expansion of , number of terms is 3 whereas the index of , is 2
 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.
 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
We now arrange the coefficients in these expansions as follows (Fig8.1):
Do we observe any pattern in this table that will help us to write the next row? Yes we do. It can be seen that the addition of 1’s in the row for index 1 gives rise to 2 in the row for index 2. The addition of 1, 2 and 2, 1 in the row for index 2, gives rise to 3 and 3 in the row for index 3 and so on. Also, 1 is present at the beginning and at the end of each row. This can be continued till any index of our interest.
We can extend the pattern given in Fig 8.2 by writing a few more rows.
Latest Jobs

 Type
 Job Notification
 Job
 KVIC Recruitment of 108 GroupB and GroupC categories  Last Date 19012020
 Location
 MumbaiMaharashtra, India
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 SAIL Durgapur Steel Plant Recruitment of Manager, Technician, Medical Service Provider  27012020
 Location
 DurgapurWest Bengal, India
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 Indian Coast Guard Recruitment 260 Navik  Last Date 02022020
 Location
 Anywhere
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 IOCL hiring 312 Apprentices  Last Date 22012020
 Location
 Anywhere
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 RBI Recruitment NEWS for 926 Assistants  Last Date 16012020
 Location
 Anywhere
 Date Posted
 7 Jan 2020

 Type
 Job Notification
 Job
 Janki Devi Memorial College Recruitment 71 Assistant Professor  Last Date 04012020
 Location
 DelhiDelhi, India
 Date Posted
 2 Jan 2020

 Type
 Job Notification
 Job
 NPCIL Recruitment of Trainee, Electrician, Fitter, Machinist, Welder, Driver  Last Date 21012020
 Location
 RawatbhataRajasthan, India
 Date Posted
 2 Jan 2020

 Type
 Job Notification
 Job
 AIIMS Nagpur 104 Principal, Lecturer, Staff Nurse. Last Date 14012020
 Location
 NagpurMaharashtra, India
 Date Posted
 2 Jan 2020

 Type
 Job Notification
 Job
 Delhi Police Recruitment of 649 Head Constable  Last Date 27012020
 Location
 DelhiDelhi, India
 Date Posted
 2 Jan 2020

 Type
 Job Notification
 Job
 IBPS Recruitment Specialist Officers 1163 Vacancies  Last Date 26112019
 Location
 Anywhere
 Date Posted
 20 Nov 2019