https://file.aiquickdraw.com/mathbot/file/1728053907413d6361zgu.jpg

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:** \( 5g^2 + 9f + 3 \)

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### 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:** \( 7g - 29 \)

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### 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:** \( 24c - 9c^3 \)

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

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**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!

Simplify, multiply, and tidy up algebraic expressions as shown in the image.

Learn how to simplify and multiply algebraic expressions with detailed step-by-step solutions. This problem involves combining like terms and applying the distributive property, making it suitable for students in Grades 7-10.

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