https://file.aiquickdraw.com/mathbot/file/1726347953331sx5fa7ic.jpg

Let's go through each problem and simplify the expressions one by one.

### 8. \( 3x(x - 2) + 7(x - 2) \)
Let's factor out the common term \((x - 2)\):
\[
3x(x - 2) + 7(x - 2) = (3x + 7)(x - 2)
\]

### 9. \( 4x(3x + 5) - 3(3x + 5) \)
Factor out the common term \((3x + 5)\):
\[
4x(3x + 5) - 3(3x + 5) = (4x - 3)(3x + 5)
\]

### 10. \( x(4x + 9) + (4x + 9) \)
Factor out the common term \((4x + 9)\):
\[
x(4x + 9) + (4x + 9) = (x + 1)(4x + 9)
\]

### 11. \( 8a - 2ab + 6ac - 4a^2 \)
Group and factor terms:
\[
8a - 2ab + 6ac - 4a^2 = 2a(4 - b + 3c - 2a)
\]

### 12. \( 15x^2 - 20x + 10 \)
Factor out the greatest common factor, which is 5:
\[
15x^2 - 20x + 10 = 5(3x^2 - 4x + 2)
\]

If you would like more detailed explanations on how each of these were simplified or factored, let me know!

### Relative Questions to Expand Understanding:
1. How do you identify a common factor in algebraic expressions?
2. What is the process of factoring a polynomial?
3. How can you use the distributive property to simplify expressions?
4. What are some strategies for factoring trinomials?
5. How does factoring help in solving equations?

### Tip:
When factoring, always look for a common factor first before attempting more complex methods like grouping or using special formulas.

Solve the algebraic expressions shown in the image for problems 8-12.

Explore how to simplify and factor algebraic expressions involving distribution, factoring common terms, and factoring quadratics. Suitable for Grades 8-10, this guide breaks down the steps to solve expressions like 3x(x - 2) + 7(x - 2) and 15x^2 - 20x + 10.

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