The Distributive Property Made Simple

The Distributive Property is a helpful tool in math, especially when you’re working on algebra in Year 8.

So, how do we use this property? Let’s break it down into easy steps!

What is the Distributive Property?

The Distributive Property tells us that if you have numbers or letters (we call them variables) like $a$, $b$, and $c$,

you can multiply them like this:

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

This means you multiply $a$ by each part inside the parentheses.

How to Use It

1. Look at the expression: Start by finding the algebraic expression you want to expand. For example, let’s say we have $3(x + 4)$.

2. Distribute: Now, use the Distributive Property. Multiply each part inside the parentheses by the number outside. Here’s how:

   • First, multiply $3$ by $x$: that gives us $3x$.
   • Next, multiply $3$ by $4$: that gives us $12$.

3. Put it all together: Now we combine what we found to make the expanded expression:

   • So, $3(x + 4) = 3x + 12$.

Example with Two Variables

Now, let’s try a slightly trickier example: $2(a + 5b)$.

1. Distribute $2$:

   • First, $2 \times a$ gives us $2a$.
   • Then, $2 \times 5b$ gives us $10b$.

2. Combine for the final answer:

   • So, $2(a + 5b) = 2a + 10b$.

Summary

Using the Distributive Property makes expanding algebraic expressions easier. Just remember to multiply each part inside the parentheses by the number outside, and then add them up.

This method not only helps you with basic equations, but it also gets you ready for more complicated algebra later on.

Happy expanding!