# 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

3

x+ 15 = 3(x+ 5)

This means that the **factors** of 3*x* + 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:

x^{2}−y^{2}= (x+y)(x−y)

### Example 3: Factoring difference of 2 squares

Factor 36*s*^{2} − 121*t*^{2}

### Exercises

Factor the following:

**(1)** 18*p*^{3} − 3*p*^{2}

**(2) **5*a* + 10*ax* − 5*ay* +
20*az*

**(3)** 36*a*^{2}*b*^{
2} − 169*c*^{2}

**(4)** (*a* −
*b*)^{2} − 1

**(5) ***y*^{4} − 81

**(6) ***r*^{2}* *− *s*^{2 }+ 2*st ** *− *t*^{2}

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