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I always like to share with my students what each Math topic has to do with their everyday life, particularly their future.

Yesterday, I did Binomial Expansion. It’s about finding the RIGHT partner (: It’s about mastering the skills of finding the correct match based on a set of factors.

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Just like this question, you see that there are 2 brackets. 1st bracket is good for now. 2nd bracket needs us to do some expansion work by using the FORMULAE (It’s provided during GCE O Level Exams but some schools don’t seem to provide it for their mid year, strange)
Oh yar, there is NO need to remember the Binomial Expansion Formulae!
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Then one of the questions that often pop up is ” When do we stop our expansion for (1+\frac {x}{3})^{12}?”

To answer this question, it depends on what type of partners you are looking for.


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We are interested in the coefficients of x & x^2 so from the first bracket :

To have x,

  • 6 will pair up with x from (1+\frac {x}{3})^{12}
  • 2x will pair up with the constant from (1+\frac {x}{3})^{12}

Similarly, to have x^2,

  • 6 will pair up with x^2 from (1+\frac {x}{3})^{12}
  • 2x will pair up with the x,from (1+\frac {x}{3})^{12}
  • -3x^2 will pair up with the constant from (1+\frac {x}{3})^{12}

Now, do you know where you stop the expansion of (1+\frac {x}{3})^{12}?

Stop at the x^2 term :) aka the 3rd term

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