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The exercise you shared appears to include algebraic expressions where simplification or expansion is needed. I'll help you solve each of the expressions step by step.

Here’s a breakdown of the questions:

1. **\( 2x - 4 \)**:
   This is already simplified.

   Answer: \( 2x - 4 \)

2. **\( xy + y \)**:
   Factor out the common factor \( y \).

   Answer: \( y(x + 1) \)

3. **\( qr - 2q \)**:
   Factor out the common factor \( q \).

   Answer: \( q(r - 2) \)

4. **\( 6x - 3y \)**:
   Factor out the common factor \( 3 \).

   Answer: \( 3(2x - y) \)

5. **\( xyz + yz \)**:
   Factor out the common factor \( yz \).

   Answer: \( yz(x + 1) \)

6. **\( x^2y + 2yz \)**:
   Factor out the common factor \( y \).

   Answer: \( y(x^2 + 2z) \)

7. **\( x^3y + xy^2 \)**:
   Factor out the common factor \( xy \).

   Answer: \( xy(x^2 + y) \)

8. **\( 5qr + 10r \)**:
   Factor out the common factor \( 5r \).

   Answer: \( 5r(q + 2) \)

9. **\( 12pw^2 - 8w^2y \)**:
   Factor out the common factor \( 4w^2 \).

   Answer: \( 4w^2(3p - 2y) \)

10. **\( 55p^3 + 33p^2 \)**:
    Factor out the common factor \( 11p^2 \).

    Answer: \( 11p^2(5p + 3) \)

11. **\( 6p^4 + 8p^3 + 10p^2 \)**:
    Factor out the common factor \( 2p^2 \).

    Answer: \( 2p^2(3p^2 + 4p + 5) \)

12. **\( 10x^3y^2 + 5x^2y^3 + 15x^2y^2 \)**:
    Factor out the common factor \( 5x^2y^2 \).

    Answer: \( 5x^2y^2(2x + y + 3) \)

Would you like to dive deeper into any specific solution or need more details? 

Here are 5 related questions to explore further:

1. How do you factor polynomials with more complex terms?
2. How do you know when to stop factoring?
3. What are some techniques to handle trinomials?
4. How can we apply the distributive property in reverse for factoring?
5. What are the applications of factoring in real-world problems?

**Tip**: When factoring, always check if there is a greatest common factor (GCF) that you can factor out before diving into more complex methods!

Factor and simplify the algebraic expressions in the given image.

Solve a set of algebraic expressions through factoring and simplifying. Learn how to extract common factors, apply the distributive property, and handle higher-order polynomial expressions. Ideal for Grades 9-12 students.

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