Lesson: The Distributive Property

Introduction

The Distributive Property is a fundamental principle used to simplify expressions and solve equations. It states that for any numbers $a$, $b$, and $c$:

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

This means you can distribute (or multiply) $a$ to both $b$ and $c$.

Steps to Use the Distributive Property

1. Identify the term outside the parentheses (the multiplier).
2. Multiply the term by each term inside the parentheses.
3. Combine like terms if possible.

Example

Let's simplify the expression:
$3(x + 4)$

Step 1: Identify the multiplier, which is $3$.
Step 2: Distribute $3$ to both $x$ and $4$: $3(x) + 3(4)$

Step 3: Perform the multiplication: $3x + 12$

So, the expression $3(x + 4)$ simplifies to $3x + 12$.

Key Questions

• What does the Distributive Property allow us to do with expressions?
• Can you give an example of how to apply the Distributive Property?
• How can the Distributive Property help in solving equations?

Conclusion

The Distributive Property is a powerful tool for simplifying expressions and solving equations. Practice using it with different values for better understanding!