We are tasked with finding the sum of the two expressions:

1. $6x^2 + 10x - 76x^2 + 10x - 7$
2. $-x^2 - 8x$

Step-by-step solution:

1. Combine like terms in the first expression: $6x^2 - 76x^2 + 10x + 10x - 7$ Simplify the coefficients: $(6x^2 - 76x^2) + (10x + 10x) - 7 = -70x^2 + 20x - 7$

2. Simplify the second expression: The second expression is already simplified: $-x^2 - 8x$

3. Add the two expressions: Combine $-70x^2 + 20x - 7$ with $-x^2 - 8x$: $(-70x^2 - x^2) + (20x - 8x) - 7$ Simplify each group: $-71x^2 + 12x - 7$

Final Answer:

$\boxed{-71x^2 + 12x - 7}$

Would you like a detailed breakdown of any step or related questions? Here are some follow-ups:

1. What are the steps for combining like terms in polynomials?
2. How do negative coefficients affect polynomial addition?
3. What is the general rule for adding polynomials with different degrees?
4. Could you explain how constants (like $-7$) are handled during addition?
5. What is the importance of arranging polynomials in standard form?

Tip: Always align like terms (same power of $x$) when adding or subtracting polynomials to avoid errors.