Factorize the expression $ab-by-ay+y^2$.

Given:

The given expression is $ab-by-ay+y^2$.

To do:

We have to factorize the expression $ab-by-ay+y^2$.

Solution:

Factorizing algebraic expressions:

Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. 

An algebraic expression is factored completely when it is written as a product of prime factors.

Here, we can factorize the expression $ab-by-ay+y^2$ by grouping similar terms and taking out the common factors. 

The terms in the given expression are $ab, -by, -ay$ and $y^2$.

We can group the given terms as $ab, -ay$ and $-by, y^2$. 

Therefore, by taking $a$ as common in $ab, -ay$ and $-y$ as common in $-by, y^2$, we get,

$ab-by-ay+y^2=a(b-y)-y(b-y)$

Now, taking $(b-y)$ common, we get,

$ab-by-ay+y^2=(a-y)(b-y)$

Hence, the given expression can be factorized as $(a-y)(b-y)$.