NCERT Solutions for Class 11 Maths Chapter 8 - Binomial Theorem

In the Binomial Theorem chapter, the students will learn about binomial theorems for positive integers. This chapter throws light on the origin and history of the binomial theorem for positive integer indices along with its statement and proof. In Mathematics, binomial theorems come when complex calculations are hard to solve through repeated multiplication.

Other topics, such as the general and middle term in the binomial expansion, Pascal's triangle, and the application of the same in a simplistic manner are also covered in this chapter. The process where the power roots of the sums of two or more binomials are algebraically expanded is known as a binomial theorem. And, in the process of expanding the coefficients of binomial terms are considered as binomial coefficients. Overall, students can find two exercises plus a miscellaneous exercise in this chapter for practice. Topics covered in this chapter are:

• Introduction to Binomial Theorem

Discussing different concepts of the binomial theorem and solving simple equations is what students would study here.

• Binomial Theorem for Positive Integral Indices

Describing the four different forms of expansion, i.e. (l + m) and (l - m) to the power 2; and (l + m) and (l - m) to the power 3.

• Pascal's Triangle

• Binomial Theorem for any positive integer 'n'

Discussing the different properties of the binomial theorem in respect of any positive integer will be done in this part.

• Meaning of General and Middle Terms in Binomial expansion

Understanding the basic differences between general and middle terms in binomial theorem is a part of this topic.

• Some Special Scenarios

In this section, an explanation regarding the application of different formulas will be done.