A binomial expression is an algebraic expression that has two terms. For example: x + 15. Now when the question of expansion of expressions such as this arises, the method is pretty basic and simple till the time the powers become large and unmanageable. When the powers are large it becomes impractical to solve them using the standard expansion methods (direct multiplication).

To avoid the tediousness involved in such calculations, Binomial Theorem is used. It allows us to expand the binomials raised to larger powers with great convenience. It also assists us with the expansion of binomial expressions that are more complicated. This topic can be understood using the most basic preparation books like NCERT (CBSE books for class XI and class XII).
In this lecture a question from the topic Binomial Theorem has been discussed.

From the perspective of IIT JEE only the binomial theorem for positive integers is the one that holds any significance. It can be prepared by understanding concepts from any basic IIT books or AIEEE books.
To proceed with the expansion, the right hand side is the first one to be considered. ‘r’ is the variable term here. The common terms are cancelled for simplification as seen in the video. The solution is then proceeded with as seen in the video. It is not difficult to deal with factorials and Binomial Theorem as it might seem to the beginners. It is in fact considered to be one of the easiest topics in Algebra from the perspective of IIT JEE and other entrance examinations. Just make sure to get your hands on the right books for IIT JEE and books for AIEEE.
A long procedure leads us to the answer. These questions are lengthy to solve, thus one must make it a habit to practice ample questions of this kind from practice papers and preparation books to understand how they must be proceeded with. This would help the students save some time while writing the actual examination. One thing that must be kept in mind is to not judge this question by the length of its solution because once the conceptual fundamentals are clearly understood using proper preparation books then solving this question would be a child’s play to you.

 

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