Let's simplify the expression:

\[
(7x^2y^3 + 6 - x^3y^3) - (5x^3y^2 - 2x^3y^3)
\]

First, distribute the negative sign across the second set of parentheses:

\[
7x^2y^3 + 6 - x^3y^3 - 5x^3y^2 + 2x^3y^3
\]

Next, combine like terms:

- Combine the \(x^3y^3\) terms: \(-x^3y^3 + 2x^3y^3\) simplifies to \(x^3y^3\).
- There are no other like terms for \(7x^2y^3\), so it stays as is.
- Similarly, \(6\) stays the same.
- \(5x^3y^2\) also stays as it is.

The simplified expression is:

\[
7x^2y^3 + 6 + x^3y^3 - 5x^3y^2
\]

This is the most simplified form of the given expression.

Would you like more details, or do you have any questions?

Here are five related questions you might find interesting:

1. How would the expression change if \(y^3\) was factored out from the first two terms?
2. What if you added another term, like \(4x^2y^2\), to the original expression?
3. How would the expression simplify if \(x^3y^3\) was factored out?
4. What is the result if \(x = 1\) and \(y = 2\) are substituted into the simplified expression?
5. How does the expression change if the exponents on \(x\) are increased by 1?

**Tip:** Always distribute the negative sign carefully when simplifying algebraic expressions.

Learn how to simplify the algebraic expression (7x^2y^3 + 6 - x^3y^3) - (5x^3y^2 - 2x^3y^3) step-by-step. This problem involves combining like terms and distributing negative signs. Suitable for Grades 7-9.

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