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

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

If in doubt, use the grid method

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

If in doubt, use the grid method

If you are asked to expand , this means work out

If in doubt, use the grid method

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

F:

O:

I:

L:

Use the technique which works for you!

Harder looking expansion: expand