https://file.aiquickdraw.com/mathbot/file/1726197995082ddyr16g9.jpg

The problem shown in the image involves adding two polynomials:

\[
(7x^7y^8 - 5x^5y^5 - 3xy) + (4x^7y^8 - 6x^5y^5 + 4xy)
\]

### Step-by-step solution:

1. **Identify like terms**: These are terms that have the same variables raised to the same powers.
   - \(7x^7y^8\) and \(4x^7y^8\) are like terms.
   - \(-5x^5y^5\) and \(-6x^5y^5\) are like terms.
   - \(-3xy\) and \(4xy\) are like terms.

2. **Add the like terms**:
   - \(7x^7y^8 + 4x^7y^8 = (7 + 4)x^7y^8 = 11x^7y^8\)
   - \(-5x^5y^5 + (-6x^5y^5) = (-5 - 6)x^5y^5 = -11x^5y^5\)
   - \(-3xy + 4xy = (4 - 3)xy = 1xy = xy\)

3. **Write the final result**:
   \[
   11x^7y^8 - 11x^5y^5 + xy
   \]

This is the simplified expression after adding the given polynomials.

Would you like any further details on this process?

### Follow-up Questions:
1. What happens when adding polynomials with no like terms?
2. How do you identify like terms in a polynomial?
3. Can polynomials with different powers of \(x\) or \(y\) ever be added together?
4. How do coefficients affect polynomial addition or subtraction?
5. Can you subtract polynomials following the same method?

**Tip**: Always align terms with the same powers when adding or subtracting polynomials to ensure accuracy.

(7x^7y^8 - 5x^5y^5 - 3xy) + (4x^7y^8 - 6x^5y^5 + 4xy)

Learn how to add the polynomials (7x^7y^8 - 5x^5y^5 - 3xy) and (4x^7y^8 - 6x^5y^5 + 4xy) step by step. This solution involves identifying like terms and simplifying them for a final result. Suitable for students in Grades 8-10.

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