https://file.aiquickdraw.com/mathbot/file/1725999934916w7uf1gp4.jpg

Let's solve the expression:

\[
(3a^5b + 7ab^2 + 11a^4b^3) - (-2ab^2 + 3a^5b + a^4b^3)
\]

### Step 1: Distribute the negative sign.
When we subtract, we distribute the negative sign to each term inside the parentheses:

\[
(3a^5b + 7ab^2 + 11a^4b^3) + (2ab^2 - 3a^5b - a^4b^3)
\]

### Step 2: Combine like terms.

- For the \(a^5b\) terms: \(3a^5b - 3a^5b = 0\)
- For the \(ab^2\) terms: \(7ab^2 + 2ab^2 = 9ab^2\)
- For the \(a^4b^3\) terms: \(11a^4b^3 - a^4b^3 = 10a^4b^3\)

### Step 3: Final result.

After combining all like terms, the expression simplifies to:

\[
9ab^2 + 10a^4b^3
\]

Thus, the correct answer is:

\[
\boxed{d}
\]

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Would you like any additional details or have any questions?

Here are 5 related questions to further explore the concept:
1. How would the answer change if the sign on the first \( a^5b \) term were negative?
2. What happens if we add another term involving \( a^6b \) to the original expression?
3. How would this expression change if \( a \) and \( b \) were specific numbers?
4. Can you generalize how to combine terms in polynomials with more variables?
5. What if the exponents on \( a \) and \( b \) were fractions?

**Tip:** When combining like terms, always ensure that both the variable parts and exponents match exactly.

(3a^5b + 7ab^2 + 11a^4b^3) - (-2ab^2 + 3a^5b + a^4b^3)

Learn how to simplify the polynomial expression (3a^5b + 7ab^2 + 11a^4b^3) by combining like terms. This problem demonstrates key algebraic concepts in polynomial simplification and is suitable for students in Grades 8-10.

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