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I see that you've uploaded an image containing several algebraic expressions and equations. Let me solve each one for you.

1. **(4x + 5)(3x - 2) =**  
   \[
   (4x + 5)(3x - 2) = 4x(3x) + 4x(-2) + 5(3x) + 5(-2) = 12x^2 - 8x + 15x - 10 = 12x^2 + 7x - 10
   \]

2. **w² - 6w - 7 = ( \_\_\_\_\_ )( \_\_\_\_\_ )**  
   We need to factor the quadratic:
   \[
   w^2 - 6w - 7 = (w - 7)(w + 1)
   \]

3. **m² + 8m + 15 = ( \_\_\_\_\_ )( \_\_\_\_\_ )**  
   Factor the quadratic:
   \[
   m^2 + 8m + 15 = (m + 5)(m + 3)
   \]

4. **x² - 49 = ( \_\_\_\_\_ )( \_\_\_\_\_ )**  
   This is a difference of squares:
   \[
   x^2 - 49 = (x - 7)(x + 7)
   \]

5. **2x² - 10x = 0**  
   Factor out the common factor:
   \[
   2x(x - 5) = 0
   \]
   Solving each factor:
   \[
   x = 0 \quad \text{or} \quad x = 5
   \]

6. **(4x + 11)² = 0**  
   Take the square root of both sides:
   \[
   4x + 11 = 0 \quad \Rightarrow \quad 4x = -11 \quad \Rightarrow \quad x = -\frac{11}{4}
   \]

7. **(2x - 5)(x + 7) = 0**  
   Set each factor to zero:
   \[
   2x - 5 = 0 \quad \Rightarrow \quad x = \frac{5}{2}
   \]
   \[
   x + 7 = 0 \quad \Rightarrow \quad x = -7
   \]

### Summary of Solutions:

1. \( 12x^2 + 7x - 10 \)
2. \( (w - 7)(w + 1) \)
3. \( (m + 5)(m + 3) \)
4. \( (x - 7)(x + 7) \)
5. \( x = 0 \) or \( x = 5 \)
6. \( x = -\frac{11}{4} \)
7. \( x = \frac{5}{2} \) or \( x = -7 \)

Would you like any more details or have any other questions?

### Related Questions:
1. How do you determine the factors of a quadratic equation?
2. Can you explain the difference of squares in more detail?
3. What is the general approach to solving a quadratic equation?
4. How do you solve a quadratic equation by completing the square?
5. What are some common errors to avoid when factoring quadratic expressions?

### Tip:
Always double-check your factoring by expanding the factors back out to ensure they match the original expression.

Solve the following algebraic expressions and equations as shown in the image.

Step-by-step solutions for algebraic expressions and quadratic equations, including factoring, the difference of squares, and solving quadratic equations. Ideal for students in Grades 8-10.

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