Factorize:

a²x² + axy + abx + by

Given a²x² + axy + abx + by = (ax × ax + ax × y + b × ax + b × y )

Taking ax common from 1^st and 2^nd term and b from 3^rd and 4^th,

a²x² + axy + abx + by = ax (ax + y) + b (ax + y)

⇒ a²x² + axy + abx + by = (ax + y) (ax + b)