2. Common Factor and Difference of Squares
Factoring means writing an expression as the product of its simplest factors.
Number example:
14 = 7 × 2
[7 and 2 are the simplest factors of 14].
Algebra example:
3x + 15 = 3(x + 5)
This means that the factors of 3x + 15 are
3 and
(x + 5)
Here is a LiveMath document to illustrate this process.
To be able to factor successfully, we need to recognise the formulas from Section 1. So it is a good idea to learn them well!
Factoring Difference of Two Squares
Example:
Factor 
Exercises:
Factorise the following:
(1)18p3 − 3p2
(2) 5a + 10ax − 5ay+ 20az
(3) 36a2b 2− 169c2
(4) (a − b)2− 1
(5) y4 − 81
(6) r2 − s2 + 2st − t2
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