The problem asks us to factorise the expression $2ab + xy - 2ay - bx$ completely.

1. Problem Description

The problem asks us to factorise the expression $2ab + xy - 2ay - bx$ completely.

2. Solution Steps

To factorise the given expression, we can use the grouping method.

First, rearrange the terms:

$2ab - 2ay - bx + xy$.

Group the first two terms and the last two terms:

$(2ab - 2ay) + (-bx + xy)$.

Factor out the common factors from each group:

$2a(b - y) - x(b - y)$.

Now, we can see that $(b - y)$ is a common factor in both terms:

$(2a - x)(b - y)$.

This is the completely factorised form.

3. Final Answer

$(2a - x)(b - y)$