# Factorising an algebraic expressions

## Basic Concept

#### Factorisation

Example 1

Factorise $$20 + 10x$$

Solution:

Both 20 and $$10x$$ can be divided by 10, therefore the Highest Common Factor (HCF) = 10.

$$20 + 10x = 10(2 + x)\:\:\:\:\:\color {red} \text{take out common factor 10}$$

Example 2

Factorise $$21ab - 14bc$$

Solution:

Both $$21ab$$ and $$14bc$$ can be divided by 7b, therefore the Highest Common Factor (HCF)= $$7b$$.

$$(21ab - 14bc = 7b(3a - 2c)\:\:\:\:\:\color {red} \text{take out common factor 7b}$$

Example 3

Factorise $$2a(p-q) - 5(p-q)$$

Both $$2a(p-q)$$ and $$5(p-q)$$  can be divided by $$(p-q)$$ therefore the Highest Common Factor (HCF) =  $$(p-q)$$

$$2a(p-q) - 5(p-q) = (p-q)(2a - 5)\:\:\:\:\:\:\color {red} \text{take out common factor } (p-q)$$