In this post, I’ll share with you a summary of binomial expansion based on the O Level Additional Mathematics syllabus. You can find what’s covered in binomial expansion in this article.
There’s really nothing much to memorize for binomial expansion. Everything you need is in your formula booklet. You just need to know where to look for them. I cover this in my O Level Additional Math course which you can find here.
Basically for binomial expansion, you need to know how to expand a binomial series (or make something looks like a binomial so that you can apply the formula) or find a particular term.
Binomial Expansion Formula
For powers of n which are positive integers, the following is the binomial expansion:
(a+b)n = an + nC1an-1b + nC2an-2b2 + .. + nCran-r br+ bn
Term Formula in Binomial Expansion
Sometimes, instead of asking you to expand the expression, you are asked term independent of x, or terms with x2 and so on. To do so, you can use the term formula:
(r+1)th term = nCran-r br
A visual summary of binomial expansion can be found here:
Want to learn O Level Additional Mathematics on-demand?
Mathematics is all about applying and being able to do questions. Apart from knowing these notes and formulae, you must also be familiar with how to apply them to the questions. The nice thing about Additional Mathematics is the questions are quite standard.
For instance, there are generally 2 main types of questions for binomial expansion tested in O Level Additional Mathematics – one is on expansion and another is on finding a particular term. There are also some commonly asked questions that I tell students to memorize (something short) so that they can do their papers faster.
In my course, I go into detail not only the concepts but how to apply them. We also go through many questions together step-by-step, so that students finish the course equipped with the skills needed to tackle their test and exam questions with confidence. You can get the course here.