Sign up now
to enroll in courses, follow best educators, interact with the community and track your progress.
L1 Introduction to Binomial Theorem and Illustrations (in Hindi)
714 plays

In this lesson we have discussed some of the important concepts of Binomial Theorem.

Ashish Bajpai is teaching live on Unacademy Plus

Ashish Bajpai
BTech|| MBA || You Tuber ,Detailed lectures will make you love , feel and enjoy Maths. The more you will learn ,will have thirst for more.

Unacademy user
Very useful video mam please continue this style of creativity And reduce background disturbance
sir plz reply, i found ur profile today , ur courses look awesome, sir my physics and chemistry is almost prepare but im very weak in maths i had not practiced anything as i dont found a maths teacher before, but today i founded ur profile, sir i request u plz can u tell me which of ur courses in maths i should do so as to score minimum 60 marks in jee main , sir i have 20 days in my hand and my target is jee main only, ur profile has so many awesome courses , so im confused, plz plz plz plz can u tell me which of ur course covers all maths lessons important questions for jee main after doing that i can solve most questions in jee main plz help, im ready to work hard in maths, hope u will tell in detail , thanks a lot for all hardwork :)
Ashish Bajpai
2 months ago
Do crash courses , and all Problem solving courses , if you are stuck in ant topic then you visit the topic in Mastering course to clear that concept , so you will have to work very hard and if you don't understand necessarily try to cover that concept from main course
Saga raga
2 months ago
but sir ur profile have many crash courses , plz can u tell specific name of ur crash courses..?
Ashish Bajpai
2 months ago
JEE Mains waale Kar lo
  1. unacademy CFollow me on the Unacademy Ashish Bajpai o Learning App 0,7% 66 5 All coorses (25) Get updates about new courses Watch all my lessons Download slides and watch offline Q Ashish Bajpai

  2. unacademy All Structured Complete Physics Weekly quizzes & live courses Chemistry & Math doubt clearing plus Ashish Bajpai Referral ID: AshishBajpai

  3. ABOUT ME O BTech in Computer Science u MBA in Finance (IBS Hyderabad) 10 Year Corporate Experience. More than 80 Courses, 1.5K+ Lessons & 32K + Followers Passion to learn and teach online. 6+ Years of Teaching Experience for IT Maths Completed 7-certifications from IVY League Universities

  4. BINOMIAL THEOREM BINOMIAL EXPRESSION Any algebraic expression which contains two dissimilar terms is called binomial expression For example x y, xy1, BINOMIAL THEOREM The formula by which any positive integral power of a binomial expression can be expanded in the form of a series is known as BINOMIAL THEOREM. + 3 etc. 1/3 x z x -y) If x, y e R and ne N, then : ( x + y Cox" + C1Xn-1 y + C2xmp + + C,x"y'+, + Cy= crx" ryr r-0

  5. Few Binomial expansions Consider two numbers a and b, then a+b a2 +2ab +b2 a+b (a+b)(a+b) (a+b).(a+b) (a+bf-( + 2ab + b2y@+2ab + b2) -(a+b) a +2ab+b2 a3 + 3a2b + 3ab2 + b3 - (a2 +2ab +b a2 +2ab +b -a4 +4a3b+6a2b2 +4ab3 +b.

  6. Some Examples Illustration: Expand (y + 2). -y12y60y4 160y3 240y2 + 192y 64. Illustration: Expand the following binomial 4 3x3 Sol: By using formula of binomial expansion.

  7. 2 4 3x 3x 3x 0 27 2 6 27 2 81 ,12 16 DEDUCTION FROM BINOMIAL THEOREM Results of Binomial Theorem D-1 On replacing a by -a, in the expansion of (xa), we get r-0 Therefore, the terms in (x-a)n are alternatively positive and negative, and the sign of the last term is positive or negative depending on whether n is even or odd.

  8. D-2 Putting x = 1 and a = x in the expansion of (x + a. we get r-0 This is the expansion of (1 + x)" in ascending powers of x. D-3 Putting a = 1 in the expansion of (x + a)", we get r-0 This is the expansion of (1x) in descending powers of x. D-4 Putting x = 1 and a =-x in the expansion of (x + ay, we get

  9. D-5 From the above expansions, we can also deduce the following Illustration: Write first 4 terms of 1 2 2y Sol:

  10. Illustration:If in the expansion of (1x)m (1 x), the coefficients of x and x2 are 3 and 6 respectively then m is (A) 6 (B) 9 (C) 12 (D) 24 (1 + x)" (1 -x)" = | 1 + mx + (m)(m -1).x 2 Sol : 2 Coefficient of x = m-n = 3 n(n 1) m(m1) Coefficietof x2mn 2 2 Solving) and (), we get m=12and n = 9.