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) =  \((p-q)\)

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