Factorize the expression $1+x+xy+x^2y$.

Given:

The given algebraic expression is $1+x+xy+x^2y$.

To do:

We have to factorize the expression $1+x+xy+x^2y$.

Solution:

Factorizing algebraic expressions:

Factorizing an algebraic expression means 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 $1+x+xy+x^2y$ by grouping similar terms and taking out the common factors. 

The terms in the given expression are $1, x, xy$ and $x^2y$.

We can group the given terms as $1, x$ and $xy, x^2y$. 

Therefore, by taking $1$ as common in $1, x$ and $xy$ as common in $xy, x^2y$, we get,

$1+x+xy+x^2y=1(1+x)+xy(1+x)$

Now, taking $(1+x)$ common, we get,

$1+x+xy+x^2y=(1+x)(1+xy)$

Hence, the given expression can be factorized as $(1+x)(1+xy)$.