QUADRATIC EQUATIONS : How to do Factorisation part.A (SPM, IGCSE, A-LEVEL...)

(Since my time is limited, so for every chapter I will skip some and only focus on parts which most of the students found problem with it. Maybe after I retire, then only I will complete those skipped parts.)


From now on we will be entering the topic of Factorisation.

First,
let's look at an example:

STOP!!!!

Like what I mentioned before,
teacher teach to let the students understand something,
not to teach to show off their knowledge,
so we should use a much simpler example:

So how to Factorise ?

Let's look at the Expansion from previous chapter:

Let me put some colours on it:

Did you realized that red parts on the left corresponded to the red on the right?
Also,
the green parts on the left corresponded to the green on the right?

Basically Factorisation is the reverse of Expansion:
(Explanation is included at below, you don't need to write so much when answering.)

RED : since we can only obtain x square from the multiplication of x and x.
GREEN : 7 can only be 1x7

Thus:

Then we think about how to add or subtract the green 1 and 7 to get the +8x at the middle:

+7x +1x = +8x

So the answer is:

Done.

After getting the Factorisation,
we can expand it back to check whether it is correct or not,
basically this type of question is like giving free exam marks for you.

Another example:

Answer:

Last example:

Answer:

The answer above actually included the explanation and some working process that we can do it in our brain,
so we don't need to write everything down during exam.

If excluding those,
I can actually answer in a line:

Next I prepared 10 questions,
please practice:

I will not provide the answer for the 10 questions above,
you just need to expand it back,
then you will know whether your answer is correct or not.

What?
Too troublesome to expand it back?

If you still don't know how to do Expansion in one line,
please read my previous chapter:
https://leonmathstuition.blogspot.com/2019/02/quadratic-equations-before-learning.html

If you still think that it is troublesome,
then I can only advice you not to be lazy.

That's all for today.

Please remember that this is just part.1,
next chapter will be part.2 .

Thank you!

End.

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Before learning Factorisation...


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