To simplify the expression:

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

we'll distribute the subtraction and then combine like terms.

Step 1: Distribute the Negative Sign

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

Step 2: Combine Like Terms

Group the terms with the same powers of $x$ and $y$:

• Terms with $x^4y^3$: $9x^4y^3 - 7x^4y^3 = 2x^4y^3$
• Terms with $x^2y$: $10x^2y + 5x^2y = 15x^2y$
• Terms with $xy$: $2xy - 7xy = -5xy$

Simplified Expression

$= 2x^4y^3 + 15x^2y - 5xy$

The expression in descending order of exponents of $x$ is:

$\boxed{2x^4y^3 + 15x^2y - 5xy}$

Would you like further clarification on any steps?

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Here are some related questions for further practice:

1. How would the result change if all $x$-terms were squared?
2. What if the subtraction was replaced by addition in the original expression?
3. How would you factor out a common term if one exists?
4. How would this expression simplify if $x = y$?
5. What would the expression look like if all terms with $y$ were set to zero?

Tip: Always organize terms in descending order to simplify reading and analyzing expressions.