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Binomial Theorem and Expression of Binomial Theorem is considered one the most difficult concept.
Properties of Binomial Theorem and Binomial Coefficient (Part 1), Properties of Binomial Theorem and Binomial Coefficient (Part 2) is considered one of the most asked concept.
150 Questions around this concept.
Which of the following is NOT a binomial expression?
For natural numbers if
:
Which of the following is NOT a Binomial Expression?
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Which one of the following is not a binomial expression?
Which of the following can NOT be expressed as a binomial theorem?
The expression
Binomial coefficient of
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Which of the following is Binomial theorem ?
Which of the following statement is wrong ?
Which of the statement is incorrect ?
An algebraic expression consisting of only two terms is called a Binomial Expression.
If we wanted to expand
But if we examine some simple expansions, we can find patterns that will lead us to a shortcut for finding more complicated binomial expansions.
On examining the exponents, we find that with each successive term, the exponent for x decreases by 1 and the exponent for y increases by 1. The sum of the two exponents is n for each term.
Also the coefficients for
where,
These patterns lead us to the Binomial Theorem, which can be used to expand any binomial expression.
For any natural number n, binomial expansion is
The combination
Properties of Binomial Theorem and Binomial Coefficient
1. If n is a natural number, then the expansion
2. In each term, the sum of the index of '
3. The sum of two consecutive binomial coefficients,
4.
So, if
Properties of Binomial Theorem and Binomial Coefficient
5. Binomial coefficients of the term equidistant from the beginning and end are equal.
Eg, second binomial coefficient from start
These are equal as
6.
7.
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