(11x^4 - 4xy + 5x^3) + (7x^4 - 10xy + 3y^3 - 25)

Let's solve the expression:

\[
(11x^4 - 4xy + 5x^3) + (7x^4 - 10xy + 3y^3 - 25)
\]

### Step 1: Combine like terms
- Combine the terms with \(x^4\):
  \[
  11x^4 + 7x^4 = 18x^4
  \]

- Combine the terms with \(xy\):
  \[
  -4xy - 10xy = -14xy
  \]

- The term with \(x^3\) stays the same:
  \[
  5x^3
  \]

- The term with \(y^3\) stays the same:
  \[
  3y^3
  \]

- The constant term is:
  \[
  -25
  \]

### Final expression:
\[
18x^4 - 14xy + 5x^3 + 3y^3 - 25
\]

Would you like further details or clarifications?

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Here are 5 related questions to expand this problem:
1. How would the expression change if you introduced \(z^2\) terms?
2. Can you factor any part of the resulting expression?
3. What happens if you substitute specific values for \(x\) and \(y\)?
4. How do you solve for \(x\) if the expression is set equal to 0?
5. How would you differentiate this expression with respect to \(x\)?

**Tip:** When simplifying expressions, always group similar terms first to avoid mistakes.

Understand how to simplify the polynomial expression (11x^4 - 4xy + 5x^3) + (7x^4 - 10xy + 3y^3 - 25) by combining like terms. This detailed solution walks through each step, including algebraic concepts and the distributive property. Suitable for students in Grades 9-12.

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