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We are asked to add the following polynomials:

\[
(9y^3 + 5y - 5) + (2y^2 - 4y + 3)
\]

Let's go step by step:

1. **Combine like terms:**

- \( y^3 \) terms: There is only one term with \( y^3 \), which is \( 9y^3 \).
- \( y^2 \) terms: There is only one term with \( y^2 \), which is \( 2y^2 \).
- \( y \) terms: \( 5y \) from the first polynomial and \( -4y \) from the second polynomial. Combine them: \( 5y - 4y = 1y \).
- Constant terms: \( -5 \) from the first polynomial and \( 3 \) from the second polynomial. Combine them: \( -5 + 3 = -2 \).

2. **Final expression:**

\[
9y^3 + 2y^2 + 1y - 2
\]

So, the sum of the polynomials is:

\[
9y^3 + 2y^2 + y - 2
\]

Would you like any further details or clarifications?

Here are 5 related questions to expand on this topic:

1. How do you subtract polynomials instead of adding them?
2. Can you explain how to multiply two polynomials?
3. What are some common mistakes when combining like terms?
4. How would you solve if asked to factor the final expression instead?
5. What happens if a term has no like term in either polynomial?

**Tip:** When combining like terms, always be mindful of the signs (positive or negative) associated with each term to avoid errors.

Add the polynomials: (9y^3 + 5y - 5) + (2y^2 - 4y + 3).

Learn how to add the polynomials (9y^3 + 5y - 5) and (2y^2 - 4y + 3) with a step-by-step solution. This problem covers key algebraic concepts like combining like terms and simplifying polynomials. Suitable for students in Grades 7-9.

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