Have a math quiz on Binomial Theorem coming up? Or are exams coming soon and you have forgotten everything you learnt about this topic? Fret not, because we are here with some quick tips – which would serve as a checklist of what you need to know about this topic.
If it is any comfort, Binomial Theorem is not really a big topic. In a full math exam paper, you wouldn’t usually get many questions on this topic, as compared to more complex topics like Trigonometry or Differentiation.
However, if you want to absolutely ACE your secondary school math exam, every mark counts – even the ‘small’ topics like Binomial! So, sit tight as we walk you through revision for Binomial Theorem:
1. Be familiar with the Pascal’s Triangle
Pascal’s Triangle is literally the origin story of Binomial Theorem. Instead of asking about Binomial Theorem, some questions straight up ask about the Pascal’s Triangle – and you are expected to know what it is.
Make sure you know what the Pascal’s Triangle refers to, and how to derive the coefficients in any row of the Pascal’s Triangle.
2. Memorise the general formula
There is really only one key formula you need to know – the binomial theorem, which is the formula used to expand the binomial expression. From that, you can also keep in mind the general term, which helps you find the (r+1)th term in the expansion.
Although it is just one formula, it can be quite complicated and tedious to apply. Hence, we cannot emphasise enough the importance of being careful and double-checking your workings!
Here are two patterns you can use quickly to check your expansions:
- As we move from one term to another term to the right in a binomial expansion, the power of a decreases by 1 while the power of b increases by 1.
- The sum of the powers of a and b always adds up to n.
As mentioned, performing binomial expansion is tedious. You want to build up your speed by being super familiar with the calculator functions that will help you expand any expressions quicker.
If you have not done binomial expansions in a long time, make sure you revise and know which buttons to press!
4. Do a wide range of questions
Conceptually, binomial theorem is quite straightforward. But the tricky part comes in the wide range of questions, some of which have rather complicated algebraic expressions. It helps to have a strong algebraic foundation – so if you have trouble with binomial theorem because of that, maybe it’s time to go back to basics and review your algebraic skills first.
Here are some ways binomial theorem questions can differ:
- Type of binomial expression (e.g. fractions, square roots, cubic)
- What the question is asking for (expand a specific number of terms, or find the coefficient)
- Order of coefficients (in ascending or descending order)
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