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Factorize the expression $1+x+xy+x^2y$.
The given algebraic expression is $1+x+xy+x^2y$.
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 $(1+x)(1+xy)$.
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