2. Common Factor and Difference of Squares

Factoring means writing an expression as the product of its simplest factors.

Example 1: Factoring a number

14 = 7 × 2

[7 and 2 are the simplest factors of 14. We can't break it down any more than this.]

Example 2: Factoring an algebraic expression

3x + 15 = 3(x + 5)

This means that the factors of 3x + 15 are

3, and

(x + 5)

To be able to factor successfully, we need to recognise the formulas from Section 1. So it's a good idea to learn those formulas well!

Factoring Difference of Two Squares

To factor the difference of 2 squares, we just apply the formula given in Section 1 - Special Products in reverse. That is:

x2y2 = (x + y)(xy)

Example 3: Factoring difference of 2 squares

Factor 36s2 − 121t2

Exercises

Factor the following:

(1) 18p3 − 3p2

(2) 5a + 10ax − 5ay + 20az

(3) 36a2b 2 − 169c2

(4) (ab)2 − 1

(5) y4 − 81

(6) r2 s2 + 2st t2