Binomial expressions are algebraic expressions with two terms. The name itself explains the nature of the algebraic expression. The chapter here involves the theorem, which is prominently used for binomial expansion. The process of expanding the two-term expression like (a+b) n raised to any power 'n' to obtain the individual terms is known as binomial expansion. The issue with the binomial expansion is that smaller power like 2, 3, 4 or 5 can be handled easily, but when the power increases, it causes issues to expand by common formula or continuous multiplication. Here the Binomial Theorem proves useful.
In this chapter, learners get to know about the Binomial Theorem for positive integers. This theorem can be used to solve multiplication issues that are difficult to solve. This chapter covers the history, definition, and demonstration of the Binomial Theorem for positive integral indices. Some of the topics discussed in this chapter include the general and middle terms in binomial expansion and their basic applications. The middle term of any binomial expression and how to find them is also covered in this chapter. There are two methods for determining the midterm. The middle term in expanding (x + a) n is (n/2 + 1) the terms if n is even. In the expansion of (x + a) n , the intermediate terms are (n + 1) / 2nd term and (n + 3) / 2nd term if n is odd. Later in the chapter, the students will learn about multinomial expansion.
The chapter provides an excellent calculation tool for the students, and it helps solve a lot of logical reasoning and technological and mathematics aptitude questions at a rapid pace. The concept that is covered in this chapter is mainly the Positive integral index binomial theorem. The binomial theorem has some significant implications, which are discussed in the chapter at a later stage. In a binomial extension, there is a general term and a middle term for which formula and derivations are given, along with solved and unsolved examples.
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