a. \( \quad 4(x+y) \)

Did you know that the expression \( 4(x+y) \) showcases one of the fundamental principles of algebra known as the distributive property? This clever little property tells us that you can multiply each term inside the parentheses by the factor outside. So, if you distribute the 4, you'll end up with \( 4x + 4y \)—simple, yet powerful! In the real world, you can often see expressions like \( 4(x+y) \) applied in scenarios like budgeting or production. For instance, if you're planning an event and know it costs 4 times the sum of guests and staff, you can easily calculate total expenses by simplifying that expression. It makes decision making and financial planning much easier!