How do you factor by grouping ax –ay – bx + by?

To factor the expression ax - ay - bx + by by grouping, follow these steps:

Group the terms in pairs: (ax - ay) and (-bx + by).

Factor out the greatest common factor (GCF) from each group:

In the first group (ax - ay), the GCF is 'a', so factor out 'a': a(x - y)
In the second group (-bx + by), the GCF is '-b', so factor out '-b': -b(x - y)
Now the expression looks like this: a(x - y) - b(x - y)

Factor out the common binomial: Both terms have a common factor of (x - y), so factor (x - y) out: (x - y)(a - b)

Thus, the factored form of the expression ax - ay - bx + by is: (x - y)(a - b).