To factor the expression $x^3 - xy^2 + x^2 - y^3$, we'll try grouping the terms to find common factors.

First, let's rewrite the expression by grouping terms:

$(x^3 - y^3) + (x^2 - xy^2)$

Now, let's factor each group:

1. Factor $x^3 - y^3$: This is a difference of cubes, which factors as: $x^3 - y^3 = (x - y)(x^2 + xy + y^2)$

2. Factor $x^2 - xy^2$: We can factor out $x^2$ from this term: $x^2 - xy^2 = x^2(1 - y^2)$ Notice that $1 - y^2$ is a difference of squares: $1 - y^2 = (1 - y)(1 + y)$ So: $x^2 - xy^2 = x^2(1 - y)(1 + y)$

Now, let's combine the factored groups:

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

Notice that the expression still contains terms that are not factored completely. However, this is the simplest form we can achieve by grouping. This expression doesn't factor nicely into a single simple product.

So the factored form is:

$\boxed{(x - y)(x^2 + xy + y^2) + x^2(1 - y)(1 + y)}$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you factor the expression $x^3 + y^3$?
2. What is the difference of cubes formula, and how is it applied?
3. How can you factor $a^2 - b^2 + a - b$?
4. What is the process for factoring a polynomial by grouping?
5. How would you factor the expression $x^2y - y^3 + x^2 - xy$?

Tip: Always check if the terms can be grouped in different ways to see if more simple factors can be obtained.