The given mathematical expression is:

$7x^2y + 3xy^2 - 9xy + 5x^2y^2 + 4xy^2 + 2x^2y^2 - x^2y + xy^2 + 10xy$

Let's simplify this expression by grouping like terms.

Step 1: Group similar terms

Group terms with the same variables and powers:

• Terms involving $x^2y$: $7x^2y - x^2y$
• Terms involving $x^2y^2$: $5x^2y^2 + 2x^2y^2$
• Terms involving $xy^2$: $3xy^2 + 4xy^2 + xy^2$
• Terms involving $xy$: $-9xy + 10xy$

Step 2: Combine like terms

• $x^2y$: $7x^2y - x^2y = 6x^2y$
• $x^2y^2$: $5x^2y^2 + 2x^2y^2 = 7x^2y^2$
• $xy^2$: $3xy^2 + 4xy^2 + xy^2 = 8xy^2$
• $xy$: $-9xy + 10xy = xy$

Step 3: Write the simplified expression

The simplified expression is:

$6x^2y + 7x^2y^2 + 8xy^2 + xy$

Would you like additional details on how terms were grouped or combined? Let me know if you have further questions!

Related Questions:

1. How do you factorize terms in an expression like this one?
2. What is the degree of the simplified polynomial?
3. Can we further simplify or factorize $6x^2y + 7x^2y^2 + 8xy^2 + xy$?
4. What does each term represent geometrically (if visualized as a 3D plane)?
5. How do polynomials like this relate to systems of equations?

Tip:

When simplifying, always look for terms with identical variable combinations (same variables raised to the same powers).