Recognise the difference of two squares
. Spot it whenever you see one square subtracted from another, e.g. .
Expanding means multiply every term; factorising is the reverse
To expand multiply by both terms. For two brackets multiply each term in the first by each in the second (four products), then collect like terms. Factorising puts an expression back into brackets.
Always take out the highest common factor first
Before anything else, factor out the largest number and the lowest power of each letter common to every term, e.g. .
Drawn from real examiner reports.
Putting the signs the wrong way round when factorising a quadratic
A correct factor pair is chosen but the signs are swapped, so the brackets expand back to the wrong expression — e.g. giving when was needed.
Slips when expanding, especially with negatives
Mis-multiplying a term (e.g. writing instead of ) or failing to combine signed like terms such as .
Not factorising fully — losing a common factor
With the difference of two squares, students forget a numerical factor, e.g. writing (which loses the factor of 4) instead of .
Check factors by expanding them back out
Examiners recommend multiplying your brackets out again as a quick self-check — it instantly catches a sign in the wrong place.
First thing to do when told to "factorise fully"?
Factorise fully .
