Factoring the Expression: 4x^(2)y^(2)3xy+2x2y
This expression represents a quadratic equation with two variables, x and y. Factoring this expression involves breaking it down into simpler expressions that can be multiplied together to get the original expression. Here's how we can approach it:
Grouping and Factoring

Group Similar Terms: Group the terms with similar variables together: (4x^(2)  3xy + 2x) + (y^(2)  2y)

Factor Out Common Factors:
 From the first group: x(4x  3y + 2)
 From the second group: y(y + 2)

Combine Factored Expressions: This gives us the factored form: x(4x  3y + 2)  y(y + 2)
Simplifying (Optional)
While the expression is already factored, we can try to simplify it further by looking for patterns or common factors. However, in this case, there isn't a straightforward simplification that can be done.
Conclusion
The factored form of the expression 4x^(2)y^(2)3xy+2x2y is x(4x  3y + 2)  y(y + 2).
Important Note: Factoring expressions helps us analyze and solve equations involving multiple variables. It's a fundamental skill in algebra and can be applied to various mathematical problems.