Question

How do you factor completely `a^2 - ab - a + b`?

Answer 1

`=color(green)( (a -1 ) ( a -b)`

Explanation:

`a^2 - ab - a + b`

Factorising by grouping:

We can factor this expression by making groups of two terms:
`(a^2 - ab) + ( - a + b)`

`a` is common to both the terms in the first group, and `-1` is common to both the terms in the second group:

`= a( a -b) - 1(a-b)`
`a-b` is common to both the terms now:

`=color(green)( (a -1 ) ( a -b)`