Class 11 Maths Chapter 8 | Binomial Theorem | Question 3 Explained // NCERT MATHS // Ex :- 8.1

Описание: Class 11 Maths Chapter 8 | Binomial Theorem | Question 3 Explained // NCERT MATHS // Ex :- 8.1
Class :- 11th, Ch :- 8th, Binomial Treorem ( द्विपद प्रेमय ) // Introduction // Best explanation
Class - 11th Ex :- 7.4 {Q7, Q8 } CH - 7 Permutation & Combination ( क्रमचय और संचय) NCERT BOOKClass - 11th Ex :- 7.4 { Q5 } CH - 7 Permutation & Combination ( क्रमचय और संचय) NCERT BOOKClass - 11th Ex :- 7.3 { Q10, Q11 } CH - 7 Permutation & Combination ( क्रमचय और संचय) NCERT BOOK
Class - 11th Ex :- 7.3 { Q0:- 7th } CH - 7 Permutation & Combination ( क्रमचय और संचय) NCERT BOOK
Class - 11th Ex :- 7.3 { Q5 & Q6 } CH - 7 Permutation & Combination ( क्रमचय और संचय) NCERT BOOK
Class - 11th Ex :- 7.3 { Q3 & Q4 } CH - 7 Permutation & Combination ( क्रमचय और संचय) NCERT BOOK

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Chapter: Binomial Theorem (Class 11)

The Binomial Theorem is an important topic in algebra that deals with the expansion of powers of a binomial expression, i.e., expressions of the form , where is a positive integer.

Concept:

The Binomial Theorem provides a formula to expand without multiplying the binomial repeatedly.
According to the theorem:

(a + b)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r

where
is called a binomial coefficient.

Key Points:

1. General Term:
The term in the expansion is given by



T_{r+1} = \binom{n}{r} a^{n-r} b^r

2. Number of Terms:
The expansion of has (n + 1) terms.


3. Middle Term(s):

If is even → one middle term: th term

If is odd → two middle terms: \frac{n+1}{2}th and \frac{n+3}{2}th terms



4. Special Cases:

For : expansion of

Useful in approximations when is small.



5. Applications:

Simplifying algebraic expressions

Finding coefficients of specific terms

Used in probability, statistics, and calculus.





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Summary:

The Binomial Theorem makes it easy to expand powers of binomials using binomial coefficients instead of manual multiplication. It’s a foundational concept linking algebra, combinatorics, and higher mathematics.


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