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.