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


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

To do:

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


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,


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


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

Updated on: 05-Apr-2023


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