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 = ⁿC₀ aⁿ + ⁿC₁ an - 1b + ⁿC₂ a n – 2b 2 + ...+ ⁿC_{n – 1}a.b^{n - 1} + ⁿC_n bⁿ where n is a positive integer and a, b are real numbers and 0 < r ≤ n.
• (a + b)ⁿ = k = 0k = nⁿC_k a^n-k b^k
• ⁿC_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 = ⁴C₀ (100)⁴ - ⁴C₁ (100)³ 3 + ⁴C₂ (100)² 3² - ⁴C₃ (100)¹ 3³ + ⁴C₄ 3⁴

= 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 = ⁸C₅ x^(8-5) (3y)⁵

= 56 (x³) (243 y⁵)

= 13608 x³y⁵

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.