factorise \( a-b+a b-1 \)

To factor the expression \( a - b + ab - 1 \), we can rearrange it as \( ab - b + a - 1 \). By grouping terms, we rewrite it as \( b(a - 1) + (a - 1) \). Now, we can factor out the common term \( (a - 1) \): \[ = (a - 1)(b + 1) \] So, the factored form is \( (a - 1)(b + 1) \). Additionally, if we wanted to check our work, we could expand \( (a - 1)(b + 1) \) back out to ensure it returns us to the original expression. This verification can be a handy technique in algebra!