Expansion and factorisation of quadratic equations

Hi, this is my blog on Expansion & Factorisation of Quadratic Expressions. First, let's start with some basics. 

Did you know? The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x²).

a, b and c are known values. a can't be 0.

"x" is the variable or unknown (you don't know it yet)

This is one example of how to solve a quadratic equation.

Here are some examples of quadratic equations. Try filling in the blanks and solving them yourself!

------------------------------------------------------------------------------

Now, let's move on to expansion and factorisation.

What is expansion?

We are taking terms out of brackets.

E.g. 1

3z(z+y-4)-(y+3)(z+1)

=(3z^2+3zy-12z)-(zy+y+3z+3)

=3z^2+3zy-12z-zy-y-3z-3

=3z^2+2zy-12z-y-3

E.g. 2

-(2+g-g^2)+(6g-g^2)

=-2-g+g^2+6g-g^2

=-2+5g

Let's practice!

---------------------------------------------------------------------

What is factorisation?

Find what to multiply to make the Quadratic Equation

You need to put common factors outside and put the rest in brackets.

Factorise Single brackets

- Factorise brackets by dividing out a common factor from each term

2 step factorising

- Factorise a quadratic by factorising groups of terms first

^{a2 + 6a + 4a + 24}

Factorise a Quadratic

- List the factors of the constant term & select the pair which add to the coefficient of x.

Factorise a² + 7a + 10

Factorise a² - 2a - 8

Quadratics with a common factor

- Always check for a common factor which can be divided out first

Factorise 3a2 - 9a - 30

The difference between squares

- Two squares subtracted can be factorised easily

Factorise a2 - 81
Factorise 16a4 - 49y2

Factorised Quadratics

- A factorised quadratic is solved by making each bracket = 0 Solving Quadratics

------------------------------------------------------------------------------

What is the difference?

In fact, Expanding and Factoring are opposites:

Factorisation can be like trying to find out what ingredients went into a cake to make it so delicious. which is sometimes not obvious at all!

Let's practice!

Easy? Let's have a test!

Now, let's combine these two concepts!

 

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

If not, then check out this video. It will surely help!

http://youtu.be/crTwYg7s-gA

Ok, now I think you better take a rest......

------------------------------------------------------------------------------

Refreshed? Let's move on to the adorable quadratic formula!

Just plug in the values of a, b and c, and do the calculations.

Now, you are probably like this:

Ok relax, we will do it step by step.

First of all what is that plus/minus thing that looks like ± ?

The ± means there are TWO answers: But sometimes you don't get two real answers, and the "Discriminant" shows why ... Discriminant Do you see b2 - 4ac in the formula above? It is called the Discriminant, because it can "discriminate" between the possible types of answer: when b2 - 4ac is positive, you get two Real solutions when it is zero you get just ONE real solution (both answers are the same) when it is negative you get two Complex solutions

Just put the values of a, b and c into the Quadratic Formula, and do the calculations.

Example: Solve 5x² + 6x + 1 = 0

Here, 5 is a,6 is b and 1 is c.

Still don't get it? Here's a song to show you.

http://youtu.be/IvXgFLV2gOk

------------------------------------------------------------------------------

Practice more of these quadratic equations because:

------------------------------------------------------------------------------

My reflections...

Personally, I thought that this chapter would be very confusing and challenging when I first saw the equations and formulas. Also because I had not done well in the first mathematics test of the year as I did not understand the first chapter I learnt this year. However, when I started to learn it, I realised that it was not as challenging as I had thought, once I got the formula and methods right, the two chapters were not a problem! This is also thanks to the quadratic formula song that my mathematics teacher showed us during her lesson. Although the class laughed at some parts of the song like "over 2a......", it really helped me to remember the quadratic formula well. I am really happy that I have a chance to create this blog about the expansion and factorisation of quadratic equation as it helps me to recap what I have learnt and also help others to learn about these chapters. I do hope that others who come across my blog would be enriched by it and do well in mathematics.

------------------------------------------------------------------------------

Now, don't you feel like...

Congratulations! You just learnt everything about Expansion & Factorisation of Quadratic Expressions!

Thank you and God bless!

Huang Tian Rui 2014