Let me analyze the image for the mathematical content and provide solutions. One moment, please.Here’s the breakdown of each question and its correct answer with an explanation:

1. $8x - 3x - x$:
   Simplify:
   $8x - 3x - x = 4x$.
   Correct answer: A.

2. $a^2 + a^2$:
   Combine like terms:
   $a^2 + a^2 = 2a^2$.
   Correct answer: C.

3. $5xy^2$:
   The problem does not specify simplification or context, so assume no further work. Correct answer matches:
   D: $5x \times y \times y$.

4. $-4x + 5x$:
   Simplify:
   $-4x + 5x = x$.
   Correct answer: A.

5. $2(x - 7) + x$:
   Distribute and simplify:
   $2x - 14 + x = 3x - 14$.
   Correct answer: B.

6. $-7a \times 4$:
   Multiply:
   $-7a \times 4 = -28a$.
   Correct answer: D.

7. $-9xy - 4y$:
   No further factoring possible, just simplify:
   Correct answer: A: $-36y$.

8. If $b$ is a factor of $ab + bc$, the other factor is:
   Factor $b$:
   $ab + bc = b(a + c)$.
   Correct answer: D.

9. $-30ab \div 10ab$:
   Simplify:
   $-30ab \div 10ab = -3$.
   Correct answer: A.

10. $x(x - 5)$:
    Expand:
    $x^2 - 5x$.
    Correct answer: B.

11. $30 \div 2n + 10$:
    Factor out $10$:
    $10(3 + 2n)$.
    Correct answer: D.

Would you like more details for any specific solution? Let me know!

Five Related Questions:

1. How do you factorize quadratic expressions such as $x^2 + 5x + 6$?
2. What are the rules for simplifying algebraic expressions involving exponents?
3. How do you determine if a term can be factored out of an expression?
4. What are the common mistakes when simplifying like terms?
5. How do you solve linear equations like $2x + 7 = 15$?

Tip:

Always combine like terms (variables and constants) before attempting further operations like factoring or distributing.