https://file.aiquickdraw.com/mathbot/file/172578606697087t1025v.jpg

Let's work through the exercise from the image step by step.

### Exercise 1:

1. **\( 2x - 4 \)**:
   \[
   \boxed{2x - 4}
   \]

2. **\( xy + y \)**:
   Factor the common term \( y \):
   \[
   xy + y = y(x + 1) \quad \boxed{y(x + 1)}
   \]

3. **\( qr - 2q \)**:
   Factor out the common term \( q \):
   \[
   qr - 2q = q(r - 2) \quad \boxed{q(r - 2)}
   \]

4. **\( 6x - 3y \)**:
   Factor out the common term \( 3 \):
   \[
   6x - 3y = 3(2x - y) \quad \boxed{3(2x - y)}
   \]

5. **\( xyz + yz \)**:
   Factor out the common term \( yz \):
   \[
   xyz + yz = yz(x + 1) \quad \boxed{yz(x + 1)}
   \]

6. **\( x^2y + 2yz \)**:
   Factor out the common term \( y \):
   \[
   x^2y + 2yz = y(x^2 + 2z) \quad \boxed{y(x^2 + 2z)}
   \]

7. **\( x^3y + xy^2 \)**:
   Factor out the common term \( xy \):
   \[
   x^3y + xy^2 = xy(x^2 + y) \quad \boxed{xy(x^2 + y)}
   \]

8. **\( 5qr + 10r \)**:
   Factor out the common term \( 5r \):
   \[
   5qr + 10r = 5r(q + 2) \quad \boxed{5r(q + 2)}
   \]

9. **\( 12pw^2 - 8w^2y \)**:
   Factor out the common term \( 4w^2 \):
   \[
   12pw^2 - 8w^2y = 4w^2(3p - 2y) \quad \boxed{4w^2(3p - 2y)}
   \]

10. **\( 55p^3 + 33p^2 \)**:
    Factor out the common term \( 11p^2 \):
    \[
    55p^3 + 33p^2 = 11p^2(5p + 3) \quad \boxed{11p^2(5p + 3)}
    \]

11. **\( 6p^4 + 8p^3 + 10p^2 \)**:
    Factor out the common term \( 2p^2 \):
    \[
    6p^4 + 8p^3 + 10p^2 = 2p^2(3p^2 + 4p + 5) \quad \boxed{2p^2(3p^2 + 4p + 5)}
    \]

12. **\( 10x^3y^2 + 5x^2y^3 + 15x^2y^2 \)**:
    Factor out the common term \( 5x^2y^2 \):
    \[
    10x^3y^2 + 5x^2y^3 + 15x^2y^2 = 5x^2y^2(2x + y + 3) \quad \boxed{5x^2y^2(2x + y + 3)}
    \]

Would you like further details on any of the steps? Here are five related questions:

1. How do you factor quadratic expressions like \( ax^2 + bx + c \)?
2. How can the distributive property help in expanding and factoring expressions?
3. What strategies are used to factor polynomials with more than three terms?
4. How does factoring relate to solving polynomial equations?
5. Can factoring be applied to expressions with variables raised to powers higher than 2?

**Tip**: Always look for the greatest common factor (GCF) when factoring any algebraic expression—it simplifies the process!

Simplify the given algebraic expressions by factoring.

Learn how to simplify and factor algebraic expressions such as 2x - 4, xy + y, and more. This guide provides a detailed step-by-step solution using key algebraic concepts, including the distributive property and finding the greatest common factor (GCF). Suitable for students in Grades 7-10.

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