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It is important to understand the distinction between expanding and factorising.

These concepts occur across a range of Mathematical Ideas

Expanding – lots of examples

Read through each one carefully – make sure you understand each one

Key examples 1:

 means to multiply both terms in the bracket by 5

 

So,

 means multiply both terms in the bracket by 7

 

So,

 

Key point: notice how the ‘negative sign’ is retained in this case

 

 means multiply both terms in the bracket by

 

So,

                                                                                

Key point: When we multiply two negatives that part of the answer becomes positive

 

 

 

Key point: when we multiply  by  we get an

 

 

 

 

 

 

Key examples 2

    work out the bracket part first

 

     now simplify the terms

 

 

 

   work out the bracket part carefully, we are multiplying by

 

    now, be careful with the signs, remember

 

    do both brackets separately then simplify

 

 

Moving towards more advanced Quadratic Expansion

If you are asked to expand , this means multiply the brackets together

 

If in doubt, use the grid method

 

 

 

 So the answer is

 

If you are asked to expand , this means multiply the brackets together

 

If in doubt, use the grid method

 

 

 

 So the answer is

 

If you are asked to expand , this means work out

 

If in doubt, use the grid method

 

 

 

 So the answer is

 

Key point: If we multiply TWO NEGATIVES, that part of the answer becomes POSITIVE

 

We can work out these ‘simpler brackets’ more quickly using FOIL, which stands for FIRST, OUTSIDE, INSIDE, LAST. It can also be called the SMILEY FACE TECHNIQUE

 

If asked to work out

F:

O:

I:

L:

 

So the answer is

 

Use the technique which works for you!

 

Harder looking expansion: expand  

 

 

 

 

 

So the answer is