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.

LIVEMath

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 math expression

math expression

 

Exercises:

Factorise the following:

(1)18p3 − 3p2


Answer

(2) 5a + 10ax − 5ay+ 20az


Answer

(3) 36a2b 2− 169c2


Answer

(4) (a − b)2− 1


Answer

(5) y4 − 81


Answer

(6) r2 − s2 + 2st − t2


Answer



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