Factorise the following:

a³ – a²b² – ab + b³

In the given expression

Check weather there is any common factors for all terms;

None;

Regrouping the 1^st 2 terms we have,

a³ – a²b² = a²[a-b²] -------eq 1

Regrouping the last 2 terms we have,

– ab + b³ = -b[a-b²] -------eq 2

∵ we have to make common parts in both eq 1 and 2

Combining eq 1 and 2

a³ – a²b² – ab + b³ = a²[a-b²] -b[a-b²]

= [a² – b][a – b²]

Hence the factors of a³ – a²b² – ab + b³ are [a² – b] and[a – b²]