(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 learning about Completing The Square.
Huh??
Is there anything to learn??
Just remember the formula can already right??
Well.... yeah.
You can solve the question by memorizing the formula,
just like how you can solve Factorisation by using calculator.
HOWEVER..........
You will waste your chance to admire the beauty of Completing The Square.
Also,
Maths is not just about a whole bunch of formula only!
I met a lot of people who only memorized and just relied on formula,
after they graduated,
they looked for the formula to be successful in life,
only to find out that LIFE IS NOT JUST ABOUT FORMULA ONLY.
Oooops......
Let's get back to today's topic.
Before start learning about CTS (Completing The Square),
we need to mention about Perfect Square.
What is Perfect Sqaure?
Well,
let us look at some examples of Perfect Square Number:
4, 9, 16 are all Perfect Square Number,
because those numbers are from the multiplication of the same number.
Next,
let's have a look at examples of Perfect Square Quadratic:
The above 3 quadratics are all Perfect Square Quadratic,
since it all came from the multiplication of the same algebra.
Do everyone still remember about this formula that we learnt at secondary lower syllabus:
Looks complicated.
If you don't really understand the formula,
it will be a little hard to memorize it.
Well actually if you really understand it,
you will remember it automatically.
Let me explain it:
(If we do the expansion normally without using the formula above)
For the 1st example,
x+3 can be seen as x and +3,
then x multiply with x, +3 multiply with +3,
thus we get the red parts.
Then x multiply with +3, add itself again,
thus we get the green part which is +6x.
Since we were adding the same +3x,
so we can do it as x multiply with +3, then multiply with 2 to get the +6x.
That's why 2ab is at the middle of the formula.
You will automatically remember the formula if you really understand it:
For the 2nd example,
just look at the x and -4 separately,
then x square, -4x multiply with 2 get -8x, lastly the square of -4 is 16.
DONE.
No need memorize also able to expand it within one line.
Same like always,
expand the 10 questions below each in one line:
Answer:
All the 10 answers above are all Perfect Square Quadratic.
After learning about the Expansion of Perfect Square Quadratic,
is time to learn about Factorisation too.
Example:
Answer:
First,
we find a which is the easiest.
Then only we look for b.
Different than a,
we can't just use the 9 at the most behind to find b,
because square root of 9 can be 3 or -3.
So we use -6x which is at the middle.
And we are done with the Factorisation of Perfect Square Quadratic.
Of course,
above all are just explanation,
we don't have to write until so complicated when answering the question.
Basically we can just do it within one line:
Looking for a is very simple,
when x^2 don't have any number with it, just x^2 only,
then a is x.
After knowing that a is x,
then it is easy to find b!
Just use the +8 at the middle to divide by 2, and get +4,
then square root the 16 at behind, and get +4 or -4,
combining both,
we can conclude that b is +4.
Easy~
One more example:
Answer:
Lastly,
10 questions for exercise:
No answer will be provided.
Just use the expansion to expand your answer to check whether did you get back the same thing as the question.
That's all for today,
we will start learning about CTS in next chapter.
Thank you!
End.
Please LIKE MY Facebook Page & FOLLOW MY TWITTER to be updated with the blog.
Related articles:
Before learning Factorisation...
Factorisation part.A
Factorisation part.B
Factorisation part.C
Important Links:
CONTACT ME
ABOUT ME
MY MATHS BLOG(Chinese ver.)
MY YOUTUBE
Feel free to e-mail me if you have any problems:
leonleongmaths@gmail.com
No comments:
Post a Comment