I see that you've uploaded a photo containing several algebraic expressions to simplify by combining like terms. I'll go ahead and solve them for you:

Expression #1:

$-7 + 13x + 2x + 8$
Combine the like terms:
$13x + 2x = 15x$ So, the expression simplifies to:
$-7 + 8 + 15x = 1 + 15x$

Expression #2:

$9 + 7y - 2 - 5y$
Combine the like terms:
$7y - 5y = 2y$ So, the expression simplifies to:
$9 - 2 + 2y = 7 + 2y$

Expression #3:

$2 + 3x - 4x + 6$
Combine the like terms:
$3x - 4x = -x$ So, the expression simplifies to:
$2 + 6 - x = 8 - x$

Expression #4:

$5 + 2x + 2$
Combine the like terms:
$5 + 2 = 7$ So, the expression simplifies to:
$7 + 2x$

Expression #5:

$2(4x - 1) + x$
Distribute the 2:
$2 \times 4x = 8x \quad \text{and} \quad 2 \times -1 = -2$ So, the expression becomes:
$8x - 2 + x = 9x - 2$

Expression #6:

$6x + 2(x + 4)$
Distribute the 2:
$2 \times x = 2x \quad \text{and} \quad 2 \times 4 = 8$ So, the expression becomes:
$6x + 2x + 8 = 8x + 8$

Expression #7:

$3(x + 5) - 10$
Distribute the 3:
$3 \times x = 3x \quad \text{and} \quad 3 \times 5 = 15$ So, the expression becomes:
$3x + 15 - 10 = 3x + 5$

Expression #8:

$15x - (x - 4)$
Distribute the negative sign:
$15x - x + 4$ So, the expression simplifies to:
$14x + 4$

Let me know if you'd like further explanations on any of these steps or if you have additional questions!

Would you like to explore more problems like these? Here are some questions related to this topic:

1. How would you solve a problem with more than two like terms, such as $2x + 3y + 5x + 2y$?
2. What happens when we have to distribute a negative sign across terms in parentheses?
3. Can you explain the concept of "like terms" and why it's important in algebra?
4. How do you deal with fractions when combining like terms?
5. What are some other methods to simplify expressions besides combining like terms?

Tip: Always look for the terms that share the same variable and power, such as $x^2$ with $x^2$, or $y$ with $y$, to combine them efficiently!