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