Let's start by addressing the questions one by one from the image you've uploaded. I'll simplify each expression for you.

Question 4: Simplify each of the following:

(a) $2a + 8b + 7a - 5b$
Combine like terms:
$(2a + 7a) + (8b - 5b) = 9a + 3b$

Answer: $9a + 3b$

(b) $-4m + 3n + 7 + 6m - 4n - 10$
Combine like terms:
$(-4m + 6m) + (3n - 4n) + (7 - 10) = 2m - n - 3$

Answer: $2m - n - 3$

(c) $7x^2 + 8x + 16 - 3x^2 + 5x + 12$
Combine like terms:
$(7x^2 - 3x^2) + (8x + 5x) + (16 + 12) = 4x^2 + 13x + 28$

Answer: $4x^2 + 13x + 28$

(d) $11ab + 9 - 9ab + 4 - ab$
Combine like terms:
$(11ab - 9ab - ab) + (9 + 4) = ab + 13$

Answer: $ab + 13$

(e) $9g^2 + 3f + 2 + 6f + 1 - 4g^2$
Combine like terms:
$(9g^2 - 4g^2) + (3f + 6f) + (2 + 1) = 5g^2 + 9f + 3$

Answer: $5g^2 + 9f + 3$

Question 5: Multiply and tidy up each of the following:

(a) $2(3x + 4y + 8) + 5(7x + 9y + 3)$
Expand both terms:
$2(3x + 4y + 8) = 6x + 8y + 16$
$5(7x + 9y + 3) = 35x + 45y + 15$
Combine like terms:
$(6x + 35x) + (8y + 45y) + (16 + 15) = 41x + 53y + 31$

Answer: $41x + 53y + 31$

(b) $7(4x - 2y - 5) - 3(2x - 5y - 8)$
Expand both terms:
$7(4x - 2y - 5) = 28x - 14y - 35$
$-3(2x - 5y - 8) = -6x + 15y + 24$
Combine like terms:
$(28x - 6x) + (-14y + 15y) + (-35 + 24) = 22x + y - 11$

Answer: $22x + y - 11$

(c) $6(2a + 5b - 8) - 5(4a - 8b - 1)$
Expand both terms:
$6(2a + 5b - 8) = 12a + 30b - 48$
$-5(4a - 8b - 1) = -20a + 40b + 5$
Combine like terms:
$(12a - 20a) + (30b + 40b) + (-48 + 5) = -8a + 70b - 43$

Answer: $-8a + 70b - 43$

(d) $4(3c + 5d - 2) + 6(2c + 8d - 3)$
Expand both terms:
$4(3c + 5d - 2) = 12c + 20d - 8$
$6(2c + 8d - 3) = 12c + 48d - 18$
Combine like terms:
$(12c + 12c) + (20d + 48d) + (-8 - 18) = 24c + 68d - 26$

Answer: $24c + 68d - 26$

(e) $3(5g + 8h - 3) - 4(2g + 6h + 5)$
Expand both terms:
$3(5g + 8h - 3) = 15g + 24h - 9$
$-4(2g + 6h + 5) = -8g - 24h - 20$
Combine like terms:
$(15g - 8g) + (24h - 24h) + (-9 - 20) = 7g - 29$

Answer: $7g - 29$

Question 6: Multiply out each of the following:

(a) $5x(3x^2 - 6)$
Distribute $5x$:
$5x(3x^2 - 6) = 15x^3 - 30x$

Answer: $15x^3 - 30x$

(b) $7p(4 + 2p^2)$
Distribute $7p$:
$7p(4 + 2p^2) = 28p + 14p^3$

Answer: $28p + 14p^3$

(c) $4h(6h^2 - 5)$
Distribute $4h$:
$4h(6h^2 - 5) = 24h^3 - 20h$

Answer: $24h^3 - 20h$

(d) $8t(2t^2 + 7)$
Distribute $8t$:
$8t(2t^2 + 7) = 16t^3 + 56t$

Answer: $16t^3 + 56t$

(e) $3c(8 - 3c^2)$
Distribute $3c$:
$3c(8 - 3c^2) = 24c - 9c^3$

Answer: $24c - 9c^3$

Let me know if you need any further clarification or details!

Here are 5 follow-up questions you could explore:

1. How do you factor polynomials like $15x^3 - 30x$ once expanded?
2. Can you explain how to simplify expressions involving more variables, like $11ab + 9 - 9ab$?
3. What strategies can help when distributing negative signs in expressions like in question 5(b)?
4. How can you simplify expressions involving powers, such as $24h^3 - 20h$?
5. What is the best way to verify your work after simplifying complex expressions?

Tip: When simplifying or expanding expressions, always double-check signs (positive or negative) as they often lead to common mistakes!