Expansion & Factorisation of Quadratic Expressions

Expansion & Factorisation of Quadratic Expressions

Hello, this post is for my performance task, where I am going to share with you all the concept of this math thing-a-ma-jig. Just bear with me for a bit. Don't worry, math stuns me too. Math is challenging, isn't it? Well,

You can do it.

First of all, you need to know some basics. Quadratic expressions must have a squared variable(the letters), and have no other power above the power of 2. For example,

      

Once it's solved, you get this kind of thing:

And don't forget to always do this at any point of time:

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Expansion

What is expansion?

According to Merriam-Webster, it is a more complete and detailed written work or set of comments based on something shorter. In this case, we are trying to take terms out of brackets. Like so,

1. Multiply the 5n into all the terms int the bracket. 
2. Do the same to the 3.

There you go, that's your solution!

For both sides that are brackets,have no fear.

1. Multiply the n in the first bracket to the whole second bracket. [the red arrows]
2. Apply the same with the 2 in the first bracket. [the blue arrows]
3. Add them all up

Voila! there's your solution!

This one's slightly more detailed, if you didn't get the previous one. 

1. Multiply 3n in the first bracket to the other bracket (n+4). [the red arrows]
2. Do likewise with the 2 in the first bracket. [the blue arrows]
3. Put the first expanded ones in front [red terms] and second ones behind [blue terms].
4. collect the like terms together. 12n+2n=14n
5. Place it according to powers in front, followed by a variable, then the constant.

Finally, here's the solution!

Did you get it? If you did, apply the concept to your exercises.

If not, then check out this video. It's quite thoroughly explained.

http://www.youtube.com/watch?v=aQOg0tD9BxY

Some practice: 
Do it. 

* Beware the negative signs!

Please only do question 3 for the following

You right now:


you should probably take a break now.

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Fatorisation

Refreshed, or has your brain saturated? Either way now, it's factorisation. What is fatorisation? Again on Merriam-Webster, it is the operation of resolving a quantity into factors; also :  a product obtained by factorization.

basically, you need to put common factors outside, and the rest in brackets.

A more complicated one's like this:

1. Find the all factors of the constant [blue part]
2. The 2 factors which add up to b [red part] would be the 2 numbers in the brackets
3. if a=1

Another method would be the very lovely Quadratic Formula

Looks really complicated, doesn't it?

Believe it or not, but this formula comes in very handy.
Especially when there are large numbers in your equation.
                                 

Simply key your numbers in your calculator using this.
[remember the coefficients and the first picture? The ABC is your coefficients in your equation. They're the ABC's here too!]

Well, here's a video explaining it. If you still don't get it.

http://www.youtube.com/watch?v=kuimoHMleug

Some exercises:

*Look out for the negative signs!

 OR      

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Now that you've learnt about these,

Difference between Expansion and Factorisation

Basically, expansion is the opposite of fatorisation, and vice versa.
Its quite simple really.


Its simple really. Its one way or another.

Expansion - No brackets

Factorisation - In brackets

Simple!

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be sure you apply them concepts and don't forget,

"[The universe] is written in the language of mathematics,
and its characters are triangles, circles and other geometrical  figures,
without which it is humanly impossible to understand a single word of it." 

~Galileo Galilei

"The things of this world cannot be made known
 without a knowledge of mathematics."

~Roger Bacon, a scientist

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My reflections:

Personally, at first I felt daunted by the complicated looking terms and all, but after learning, I got the hang of it. It is true that practice makes us better at math. It has to be wired in our brain for us to be good at math. As for these chapters of expansion and factorisation, it helps us attain a high level of logical thinking, as one would need logic to figure out how it works, understanding it, and thus solving it. This helps us in life when we need to make logical decisions. Therefore, the skills learnt here are important.

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And now you finally have
Over this math subject.
Doesn't it feel like you've
?

What did I say? You did it.

Your welcome.


~Thank you!
Phoebe Rae Tan





Disclaimer: I do not own any of these pictures. You'd have to thank Google Images later.