# Higher Algebra Hall & Knight Multinational Theorem (Chapter 15) Solutions

Hall and Knight Higher Algebra Solutions for Chapter 15 ‘Multinomial Theorem’ are created by subject matter experts to help you prepare easily for tough competitive exams like JEE Mains, JEE Advanced and NEET. Multinomial Theorem is an extension of the previous chapter Binomial Theorem. It discusses how we further use the binomial theorem to obtain the expansion of a multinomial expression. The chapter explains many vital concepts like the binomial theorem, multinomial theorem, formulas, and coefficients to solve different equations. Once you will understand these concepts you will be able to answer all the chapter based questions in JEE.

Higher Algebra by Hall and Knight Chapter 15 ‘Multinomial Theorem’ consists of 1 exercise. The exercise has overall 21 questions which are obtained from the concepts of the chapter. You will be able to find the coefficients of a multinomial expansion, the coefficient of any assigned term in the multinomial expansion, the general term of a multinomial expansion, and understand where the binomial theorem should be used instead of the multinomial theorem.

Instasolv solutions for Hall & Knight Higher Algebra Chapter 15 ‘Multinomial Theorem’ ensures that you are not facing any queries in the chapter. Instasolv team works hard to give you solutions that are 100% accurate. Our subject matter experts are devoted to giving you a better learning experience with the best study material. We make sure that you are fully prepared for your exams and no obstacles come your way in solving the questions.

## Important Topics for Hall and Knight Higher Algebra Chapter 15: Multinomial Theorem

To understand all the concepts of the Multinomial Theorem in Higher Algebra By H.S. Hall and S.R. Knight, you are first required to understand Binomial Theorem.

**Binomial theorem**

It consists of 2 terms whereas a multinomial theorem consists of more than 1 term. Both the terms are described as an expression.

- For example, in the expansion of (a+b)
^{4}find the coefficient of a^{3}b. The answer to this question will be 4 because if we multiply b and b from inside 1 of the brackets we get the given term a3b and from the remaining three brackets we get the a’s. - Power of a binomial theorem can also be expanded. You can also write a binomial theorem using the summation notation.

**Multinomial Theorem**

A multinomial theorem being the extension of a binomial theorem as explained above is a description of a result of expansion in a multinomial power.

- For example if we consider (a+b+c)
^{4}the ultimate way to expand it and write it is (a+b+c) (a+b+c) (a+b+c) (a+b+c) - You need to apply the distributive law followed by simplifying the like terms.
- There are around 81 terms in the given example before collecting the like terms. This is because each term present in the first bracket has to be multiplied by the terms mentioned in the second bracket that eventually gives 9 terms. Each of these terms has to be multiplied by each term mentioned in the third bracket that gives 27 terms
- Finally, these 27 terms have to be multiplied by every term in the fourth bracket that gives 81 terms.
- Thus terms look different before following the pattern of simplification, though they seem to be identical after simplification.

### Exercise Discussion of Hall & Knight Higher Algebra Chapter 15: Multinomial Theorem

- Hall & Knight Algebra Mathematics book with solutions for Multinomial Theorem consists of a single exercise.
- The exercise comprises 21 questions that cover the crucial concepts of the chapter.
- These questions are unsolved that challenge your competitive and analytical skills for JEE Mains and NEET like exams.
- The questions that you will answer in this exercise are such as find the coefficient of x
^{23}in the expansion of (1-2x+3x^{2}-x^{4}-x^{5})^{3}, expand (1-2x-2x^{2})^{1/4}as far as x^{2}and some other questions like proving the given equations. - In case you face any problems while solving the questions, you can get online solutions for the chapter at Instasolv.
- Instasolv will provide authentic solutions to your problems that are easy to understand.

### Why Use Higher Algebra by Hall and Knight Chapter 15: Multinomial Theorem by Instasolv?

- Instasolv gives you easy access to the solutions of Hall and Knight Higher Algebra Multinomial Theorem. All the solutions are accurate and easy to understand with each step.
- Our subject matter experts use the latest study material so that you do not miss out on anything from your syllabus.
- The team that solves the questions for Elementary Algebra and Higher Algebra by Hall & Knight are professionals with years of experience in the field.
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