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# Binomial Theorem Formula Class 11

Binomial theorem formula class 11 is useful in the expansion of any power of a binomial in the form of a series. It may seem a bit confusing for students to understand at first, due to the use of multiple terms involved in it. This article explains the binomial theorem formula class 11 along with some useful tips that will help students memorize it at their fingertips.

## List of Binomial Theorem Formula Class 11

Binomial formula helps to expand the binomial expressions such as x + a, (x - (1/x))4, and so on. Students can refer to the list of binomial theorem formula class 11 provided below:

**Binomial Theorem:**(a + b)^{n}=^{n}C_{0}a^{n}+^{n}C_{1}an - 1b +^{n}C_{2}a n – 2b 2 + ...+^{n}C_{n – 1}a.b^{n - 1}+^{n}C_{n}b^{n}where n is a positive integer and a, b are real numbers and 0 < r ≤ n.- (a + b)
^{n}= k = 0k = n^{n}C_{k}a^{n-k}b^{k} ^{n}C_{k}=n!k! (n-k)!- If n is even in (a + b) n, then the middle term is given by (n/2 + 1)
^{th} - If n is even in (a + b) n, then the middle terms are given by [(n+1)/2]
^{th}and [(n+1)/2 + 1]^{th}terms.

## Applications of Binomial Theorem Formula Class 11

Binomial theorem gives an easy way to expand large numbers resulting in easier calculations. Thus, the Binomial theorem formula finds its usage in several fields. Some of the useful applications of Binomial theorem formulas class 11 are listed below :

- Binomial theorem formula class 11 is widely used in statistics and probability to do various analyses.
- The binomial theorem is also helpful in civil engineering and architecture to find the cost of huge building projects.
- The Binomial theorem formula is applied in finding probability, combinatorics, calculus, and in other important areas of math.

## Binomial Theorem Formula Class 11 Examples

**Example 1: **Compute (97)^{4}.

**Solution: **We can write: 97 = 100 – 3

(97)^{4} = (100 – 3)^{4} = ^{4}C_{0} (100)^{4} - ^{4}C_{1} (100)^{3} 3 + ^{4}C_{2} (100)^{2} 3^{2} - ^{4}C_{3} (100)^{1} 3^{3} + ^{4}C_{4} 3^{4}

= 1*(100000000) - (4 * 1000000 * 3) + (6 * 10000 * 9 ) - (4 * 100 * 27) + (81)

= 88000000 + 529200 + 81

= 88529281

**Example 2**: Find the middle term in the expansion of (x + 3y)^{8}

**Solution 2**: Since n = 8 is even, the number of terms in the binomial expansion would be n+1 = 9

Middle term would be the (n/2 +1) term = 5th Term

Fifth term of (x + 3y)^{8} = ^{8}C_{5} x^{(8-5)} (3y)^{5}

= 56 (x^{3}) (243 y^{5})

= 13608 x^{3}y^{5}

## Tips to Memorize Binomial Theorem Formula Class 11

Students can follow some of the following useful tips to memorize binomial theorem formulas class 11 effectively:

- Visualizing concepts and formulas through video content like online tutorials or educational videos will help in memorizing them better. Students can find some interactive content and apps to learn these formulas.

- Students must focus and pay complete attention while studying these formulas. Giving undivided to anything always helps in quick learning.

- In the digital age where each one of us stays close to technology, students can make use of the same to save some time and effort by downloading the formula sheets. They can apply these formula sheets as wallpapers on their devices to quickly revise them.

Students can download the printable **Maths Formulas Class 11** sheet from below.

## FAQs on Binomial Theorem Formula Class 11

### What are the Important Formulas Covered Under Binomial Theorem Formula Class 11?

The important formulas covered under binomial theorem formula class 11 are listed as follows:

- (a + b)
^{n}=^{n}C_{0}a^{n}+^{n}C_{1}an - 1b +^{n}C_{2}a n – 2b 2 + ...+^{n}C_{n – 1}a.b^{n - 1}+^{n}C_{n}b^{n}. - (a + b)
^{n}= k = 0k = n^{n}C_{k}a^{n-k}b^{k} ^{n}C_{k}=n!k! (n-k)!- If n is even, for (a + b)n the middle term is n2+ 1
- If n is odd, for (a + b)n the middle term is ( n+12) and (n+12+ 1)

### Why is it Important to Practice Various Problems Related to Binomial Theorem Formula Class 11?

Practicing various problems related to binomial theorem formula class 11 will benefit students in learning the expansion of polynomials and algebraic identities. In this article, binomial theorem formulas for positive integral indices are mentioned.

### What are the Important Concepts Covered in Binomial Theorem Formula Class 11?

The important concepts covered in binomial theorem formula class 11 will help students understand the repeated multiplication of large numbers involved in simplifying calculations. Students will also learn to find the number of terms, general term and middle term in a binomial expansion. The list of formulas and examples is given above for students to learn some important concepts.

### What is the Use of General Term in Binomial Theorem Formula Class 11?

The general term in binomial theorem formula class 11 is helpful to derive the independent term, numerically greatest term, and the term with particular power.

### How many Formulas are there in Binomial Theorem Formula Class 11?

There are around five formulas that will help students in understanding the basics of expanding large numbers and also how to find the middle term if the power of two positive numbers is even or odd. These formulas play an important role in algebra.

### How can I Memorize Binomial Theorem Formula Class 11?

Students can memorize the Binomial theorem formula class 11 with the help of the tips given below:

- Connecting mathematics to images always aids in retaining the formula in the memory. Students should strive to connect each element of the formula to an image. This will help them quickly recall the formula.
- Students must make sure that they are not distracted while studying. Hence, they must find a quiet place free from noise and distractions to practice math. Focussed attention helps to learn easily!
- Students must save the formula images as wallpapers on mobile phones and laptops for a quick revision anytime.

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