Let's solve the mathematical problems visible in the image.

Task 3: Combine Like Terms

Expression:
$6b + 9c^3 - 7c^3 - 4b - 15c^3$

1. Group like terms:

   • $6b - 4b$ (terms with $b$)
   • $9c^3 - 7c^3 - 15c^3$ (terms with $c^3$)

2. Simplify:

   • $6b - 4b = 2b$
   • $9c^3 - 7c^3 - 15c^3 = -13c^3$

Final result:
$2b - 13c^3$

Task 4: Expand and Simplify

Expression:
$(a + 7)(-4a - 8)$

1. Use the distributive property (FOIL method):

   • $a \cdot -4a = -4a^2$
   • $a \cdot -8 = -8a$
   • $7 \cdot -4a = -28a$
   • $7 \cdot -8 = -56$

2. Combine like terms:

   • $-8a - 28a = -36a$

Final result:
$-4a^2 - 36a - 56$

Would you like detailed explanations of the steps, or do you have any questions?

5 Related Questions:

1. How do you identify like terms in a polynomial?
2. What is the importance of the distributive property in algebra?
3. How would the expansion change if one of the terms had an exponent, e.g., $(a^2 + 7)(-4a - 8)$?
4. What are common mistakes when combining like terms or expanding expressions?
5. How can combining like terms simplify solving equations?

Tip: Always double-check your work when combining terms or distributing to avoid sign errors.