Factorize the expression $x^3-y^2+x-x^2y^2$.

Given:

The given expression is $x^3-y^2+x-x^2y^2$.

To do:

We have to factorize the expression $x^3-y^2+x-x^2y^2$.

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 $x^3-y^2+x-x^2y^2$ by grouping similar terms and taking out the common factors. 

The terms in the given expression are $x^3, -y^2, x$ and $-x^2y^2$.

We can group the given terms as $x^3, x$ and $-y^2, -x^2y^2$. 

Therefore, by taking $x$ as common in $x^3, x$ and $-y^2$ as common in $-y^2, -x^2y^2$, we get,

$x^3-y^2+x-x^2y^2=x(x^2+1)-y^2(1+x^2)$

$x^3-y^2+x-x^2y^2=x(1+x^2)-y^2(1+x^2)$

Now, taking $(1+x^2)$ common, we get,

$x^3-y^2+x-x^2y^2=(1+x^2)(x-y^2)$

Hence, the given expression can be factorized as $(1+x^2)(x-y^2)$.