Binomial Theorems: Definition, Rules, Sample Questions, Tips and FAQs

Quantitative Aptitude Preparation Tips for MBA 2022

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Vipra Shrivastava

Vipra ShrivastavaSenior Manager - Content

Updated on Sep 19, 2022 17:18 IST

Binomial Theorem is a way of expanding a given equation and simplifying it. We break the given equation in many different fragments based on the power. The useful application for Binomial Theorem is that when the equation's power increases, the calculation work becomes tedious. It is not easy to calculate the value of (x + y4)13 easily as that would take a long time. But by using binomial theorem, we can easily calculate its value.

What is Binomial Theorem?

Whenever an equation has been raised to high powers, it is difficult to simplify it and get the answers. Hence we simplify the given equation by breaking it into parts of each power, starting from 0. In the binomial theorem, we have two variables that are being expanded. If we use more than two variables in expansion, then the expansion is called multinomial expansion that follows a different technique.

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Parts of Binomial Theorem

Any binomial expansion has different terms as the power of a variable and consonant keeps increasing from 0. Hence binomial expansion sees the use of permutation and combination concepts. Some terminologies used in the binomial expansion are general term, middle term, independent term, numerically greatest term, and the ratio of consecutive terms.

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Different Types of Arithmetic Operations

The binomial theorem can be classified based on the power for which it is expanding. Some of the major categories are:

  • Binomial Theorem for Rational Index
  • Binomial Theorem for Negative Index
  • Multinomial Theorem (more than three variables in the equation)
  • Pascal's Triangle 

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FAQs Related to Binomial Theorem

Q: How is the binomial theorem helpful in arithmetic?

A: The binomial theorem is used to simplify the complex expanding operations that involve high finite powers. 

Q: What is multinomial expansion?

A: When the number of variables in the expansion equation is more than 3, we call it a multinomial expansion.

Q: How many middle terms are there in even number power expansions?

A: When the power is any even number that means that the total number of terms would be odd, we can get exactly one middle term for even powers.

Q: What are different types of binomial theorem based on the index?

A: The binomial theorem can be broadly classified into two parts based on the index— the binomial theorem for the rational index and the binomial theorem for the negative index.

Q: Can we find remainder using binomial theorem?

A: We can find the remainders of any given equation by using the binomial theorem. Binomial theorems can also be used to find the digits of any given number when it is powered.

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