Let's solve each problem step by step:

1. $4(2x + 5y + 3)$

Distribute the 4 to each term inside the parentheses:

$4(2x) + 4(5y) + 4(3) = 8x + 20y + 12$

So, the solution is:

$8x + 20y + 12$

2. $3y + 5y - 2x + 10x$

Combine like terms:

$(3y + 5y) + (-2x + 10x) = 8y + 8x$

So, the solution is:

$8y + 8x$

3. $2(x + 4) + 4x + 5$

First, distribute the 2 to the terms inside the parentheses:

$2(x + 4) = 2x + 8$

Now, combine all terms:

$2x + 8 + 4x + 5 = (2x + 4x) + (8 + 5) = 6x + 13$

So, the solution is:

$6x + 13$

4. $-(2x + 3y)$

Distribute the negative sign:

$-(2x) - (3y) = -2x - 3y$

So, the solution is:

$-2x - 3y$

5. $-8 - 4$

This is simple subtraction:

$-8 - 4 = -12$

So, the solution is:

$-12$

6. $7 - 10$

This is also simple subtraction:

$7 - 10 = -3$

So, the solution is:

$-3$

Would you like any more details on these solutions?

Follow-up questions:

1. What is the distributive property and how is it applied in problem 1?
2. How do you identify like terms, as shown in problem 2?
3. Why is it important to distribute correctly, as seen in problem 3?
4. How does distributing a negative sign affect the terms inside the parentheses, as in problem 4?
5. Why do we get a negative number when subtracting two positive numbers in problem 6?

Tip:

When distributing a factor, remember to apply it to every term inside the parentheses to avoid mistakes!