Personal Reflections.

PERSONAL REFLECTIONS

I feel that this topic is is not as difficult as it looks like. In the beginning I was quite confused but once i practiced it was much easier. I also feel that we have to be careful and check the answer after doing it as solving quadratic expressions can be tricky and it is very easy to make careless mistakes.This topic can be very useful while creating expression when solving word problems. I can now expand and factorise quadratic expressions without problem. In conclusion, I want to say that expansion and factorisation is an interesting topic.

Factorisation

What is factorisation???                                            

Factorisation is the reverse of expansion. Expansion is removing the brackets from an expression while factorisation is adding brackets to an expression.

e.g.

           

               x to the power of 2 + 5x+ 6 = ?                          x   + 3    |  3x

                                                                                      x    + 2    |  2x

      First we draw this and add the expression in it.           _________|____          

                                                                                     x*2 +  6  l  5x

     What I did here is that I found the factor of x*2 which is x and x and found the factors of 6 which is 2 and 3. After this you have to multiply the bottom x with the top 3 and the top x with the bottom 2 and write the answer on the other side of the line. to check your answer u have to either add or subtract 3x and 2x to get the answer below the line which is 5x. After seeing everything co-ordinates with everything, you will get your final answer. Thus the answer of this expression is (x+3)(x+2) after factorising it.

This picture shows that factoring is the reverse of expansion. 

                                  

            
                                    

What is expansion???

Expansion is a mathematical term to remove brackets from an expression.

e.g. 

     2(x + 3) = ?

To do this you have to multiply 2 with x which is equal to 2x and multiply 2 with 3 with is 6. I call this the rainbow method.In this question there are 2 rainbows. Thus the expanded answer is 2x+6. After expanding there is no brackets anymore. This is called expansion!

Now there will be two sets of brackets in an expression.

e.g.

     (x+2)(x+3) = ?

For this u first have to multiply x with x then you multiply x with 3. After that you multiply 2 with x then 2 with 3. In this question there will be 4 rainbows. Thus the answer is x to the power of 2+ 3x+ 2x + 6 and the then from here you have to simplify it. After simplifying it the answer will be x to the power of 2 + 5x+ 6. After expanding there are no more brackets now.

Now you have learned how to expand!