Expanding algebraic expressions using the distributive property is like solving a puzzle! Let’s break it down step by step so you can get the hang of it.

What is the Distributive Property?

The distributive property is a rule that helps you multiply a number or expression outside parentheses by each part inside the parentheses. Here’s the basic idea:

$a(b + c) = ab + ac$

This means you take $a$ and multiply it by both $b$ and $c$.

Example 1: Simple Distribution

Let’s try expanding the expression $3(x + 4)$. Here’s how it works:

1. Find the multiplier: In this case, it’s $3$.
2. Distribute it: That means you multiply $3$ by both parts inside the parentheses.
   • First, $3 \times x = 3x$.
   • Next, $3 \times 4 = 12$.

When we put it all together, we write:

$3(x + 4) = 3x + 12$

Example 2: More Terms

Now, let’s look at a slightly trickier example: $2(3x + 5y - 4)$.

1. Identify the multiplier: Here, it’s $2$.
2. Distribute to each piece:
   • $2 \times 3x = 6x$.
   • $2 \times 5y = 10y$.
   • $2 \times -4 = -8$.

When we combine everything, we get:

$2(3x + 5y - 4) = 6x + 10y - 8$

Practice Makes Perfect

To really get good at expanding expressions, practice is super important! Try these exercises:

1. Expand: $5(a + 2)$
2. Expand: $-3(2x - 7 + y)$
3. Expand: $4(3p + 2q - 3r)$

Conclusion

Getting the hang of the distributive property will make your math work easier and help boost your confidence with algebra. Keep practicing, and soon, expanding expressions will feel easy!