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We are given the equation \( 11x^2y^2 + a = b \), and the task is to solve for \( a \).

Let's isolate \( a \) by subtracting \( 11x^2y^2 \) from both sides:

\[
a = b - 11x^2y^2
\]

Now, let's match this to the options provided:

- **Option A**: \(\frac{b - x^2y^2}{11}\) → This is incorrect.
- **Option B**: \( 11x^2y^2 - b \) → This is incorrect, as it subtracts in the wrong order.
- **Option C**: \( b + 11x^2y^2 \) → This is incorrect because it adds instead of subtracting.
- **Option D**: \( b - 11x^2y^2 \) → This is **correct**.

Thus, the correct answer is **Option D**: \( b - 11x^2y^2 \).

Would you like a more detailed explanation or have any questions? Here are some related questions you might find useful:

1. How can you solve for other variables in similar equations?
2. What are the properties of terms with exponents like \( x^2y^2 \)?
3. How would the equation change if the coefficients were negative?
4. What happens if both sides of the equation involve \( a \) terms?
5. How do you deal with equations that involve fractions or roots?

**Tip**: When solving for a variable, always look to isolate that variable by performing inverse operations systematically.

Learn how to solve for a in the equation 11x^2y^2 + a = b. This algebra problem teaches key concepts in solving for a variable by rearranging terms. Suitable for students in Grades 8-10.

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