A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method

In the earlier post on free Math Exam Papers, we received very good response. Almost 200 copies were downloaded in less than 7 days. We have a subscriber requesting for step by step solution for the questions though we have provided the answer keys. I am sorry I am unable to provide the step by step solutions due to my busy schedule. However, subscribers can email me their workings I can assist and advice you on the incorrect workings. I hope this would be useful. Moreover, by providing the step by step solution will also not be useful as most students will perhaps take the easy way out to just "read" the solution and think that they understand them. Mastery of Mathematics is not by "reading" but it's the knowing and applying of the strategies.

I have picked up one question on Binomial Expansion (another tricky A-Math topic) for discussion. Specifically on finding Term Independent of x.

Allow me to discuss the common mistake that students make.

Most students will expand the expression term by term


  • Too time consuming
  • Higher tendency to make careless mistakes!

So the following step by step solution is what I taught my students during my A-Math Ultimate Leap Programme (For Sec 4s who still wish to join, call me @ 9685 7675. For Sec 3s, we are opening up the classes in March 2009! More info will be released in Feb. Keep reading this blog)

Features to take note:

  • General Term is applied (No memorization is required, just refer to the formula sheet if you aren't sure)
  • Constant (numbers) & variable (which is x in the question) are separated. (so that we can focus on the important part first)
  • Power of x is circled (in red) so that you focus all your attention on it. (Reduces careless mistakes too!)
  • Since this is a 4 marks question, 4 minutes is the working time to complete the solution. (Time management is part of examination techniques)

Skills required:

  • Understanding of Term Independent of x (i.e it's x to the power of 0 NOT x is zero!)
  • Usage of Binomial Formula
  • Basic application of Indice law (Observe that [pmath]{1}/{x^7}[/pmath] is rewritten as [pmath]x^-7[/pmath])

Evaluate the term which is independent of x in the expansion of clip_image002[4].

So do you do your working in a similar manner or you have your own style? I would love to hear from you if you know how to do this question initially. If no, which part did you not understand?

Related Posts:

Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)

25 Responses to A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method
  1. Cindy
    February 9, 2009 | 1:20 pm

    Hi Sir/Mdm,

    I am doing the same way as what you are doing.?

    Thanks for the alert.



  2. Karishma
    March 9, 2009 | 2:25 am

    Could you please give another example?


    prashant Reply:

    Take simple terms like (a b)square or cube


  3. huaan
    March 21, 2009 | 9:20 pm

    thanks Ms Ong! I am sec 4 now, and i guess this question is really a good revision for me!=0


  4. Reza
    June 3, 2009 | 12:25 am

    Sry but i haven't learned any of this at all in school since im following the Malaysian Add Maths Syllabus.
    Could you please enlighten me on what is this Independent term thingy ?

    Thanks in adv.


  5. CombiStudent
    September 14, 2009 | 7:28 am

    How would I find the constant term in the expansion of:

    (x^2 + (1/x^2) - 2)^10.

    This is a trinomial, but is there a way I can manipulate the expression so I can use the binomial theorem? What we just did was expand it to the 5th power and then square that to find the constant term. So we did:

    [(x^2 + (1/x^2) - 2)^5]^2.

    =S It took a while, but at least we got some number :S.


  6. gautam
    October 28, 2009 | 4:49 am

    Thanks for the alert... our teacher insrtucted us to do it in the sasme way bt thanks anyway :)


  7. The Exclamation Mark ! in Binomial Theorem
    February 25, 2010 | 11:40 pm

    [...] A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method [...]

  8. Kim
    March 11, 2010 | 2:30 am

    I didn't know how to do that sort of question before I read this because I missed lectures on binomial expansion and i understood it untill the very last line because I don't understant why that term equals that specific number?


  9. Vincy
    April 4, 2010 | 9:04 am

    Thanks a lot!!!


  10. A.U
    January 17, 2011 | 4:48 pm

    Hello, I have used the exact same method for the following question:

    Find the term which is independent of x in the expansion (x^2 - 1/3x)^9

    and I got x = 0.115

    could you please go through this and see if i got the right answer



    Ai Ling Reply:

    Bingo! Absolutely correct. Congrats!

    For everyone else, note the question is: Find the term which is independent of x in the expansion (x^2 – 1/3x)^9

    read as 'one over 3x' for the second term.


  11. A U
    January 19, 2011 | 1:19 am


    thank you very much for getting back to me and thanks for checking the answer

    much appreciated!!



  12. kreme
    April 26, 2011 | 2:36 pm

    Thank you so much! I've been trying to understand this for about 2 1/2 hours now and after seeing your example, it's all clear!
    (They don't teach this in class but it comes up in every test -.-)



    Ai Ling Reply:

    Glad my sharing is of help to you :)


  13. Quilat
    May 20, 2011 | 12:35 pm

    how did you get 191 from 18 and 4?


    MrArtilli Reply:

    Use nCr on your calculator.



  14. Moses Josiah
    July 22, 2011 | 2:59 am



  15. jiaying
    August 29, 2011 | 7:31 pm

    Thankyou so much! Finally got it after looking at your example. Wow!


  16. steliosaa
    September 11, 2011 | 8:00 pm

    Thank you! I have been trying to understand this for 3 hours. After seeing your example I understood everything. Keep up the good work.


  17. ritsi
    October 3, 2011 | 4:10 pm

    thanks alot for solving my query


  18. Kirui-Kenya
    January 11, 2012 | 4:28 pm

    wow tats great!!!


  19. Sriram S Nair
    March 27, 2012 | 11:30 am

    Thank You For Describing Each And Every Step Accuerately and precisely.I hope 18C4 Must Be More Precise.


  20. Muhammad Danish
    September 1, 2012 | 5:57 pm

    this is very easy tutorial. Thanks!


  21. blessinf
    April 16, 2013 | 4:14 pm

    havin problems please help


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