The equation provided is:
$5(2x + 3y - 2)$
We are tasked with applying the distributive property to simplify it.

The distributive property states:
$a(b + c) = ab + ac$

Step-by-step solution:

1. Distribute the $5$ to each term inside the parentheses:
   $5(2x) + 5(3y) + 5(-2)$

2. Simplify each term:

   • $5(2x) = 10x$
   • $5(3y) = 15y$
   • $5(-2) = -10$

3. Combine everything:
   $10x + 15y - 10$

Final Answer:

$5(2x + 3y - 2) = 10x + 15y - 10$

Let me know if you'd like further clarifications!

Relative Questions:

1. What is the distributive property, and how is it used in algebra?
2. How do you handle negative numbers in the distributive property?
3. Can the distributive property be used for more than two terms inside the parentheses?
4. What happens if there’s a fraction outside the parentheses instead of a whole number?
5. How do you simplify equations with variables and constants after distributing?

Tip:

Always check your work by reversing the process—factor out the distributed number to ensure the original expression matches!