GCSE revision notes

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