Distributive Property

The distributive property is actually a very simply concept to learn and apply. It will allow you to simplify something like 3(6x + 4), where you have a number being multiplied by a set of parenthesis. Let's start with a simple problem:

6(4 + 2)

Based on the order of operations, you know that anything inside parenthesis should be done first. Adding 4 + 2 is simple enough, resulting in this:

6(6)

When you see a number next to parenthesis like this, it means multiplication, so what we really have here is this (remember that * means multiplication):

6 * 6 = 36

That was easy enough, but what about a more difficult problem? Let's suppose that the 4 was really 4x, meaning 4 times the variable x. The distributive property allows you to simplify an expression like this, where you cannot just do the parenthesis and multiply.

6(4x + 2)

What this expression seems to say is that we want 6 times the sum of 4x + 2. It can also be expressed in a different way using the distributive property:

(6 * 4x) + (6 * 2)

We can do this because with 6(4x + 2), the 6 is distributed to the 4x and the 2. That expression can now be simplified to 24x + 12, which is easier to use that the original 6(4x + 2). Now try simplifying this expression:

-2(4y - 8)

This is no more difficult so simplify than the last one. Just distribute the -2 to the 4y and the -8:

(-2 * 4y) + (-2 * -8)
-8y + 16
16 - 8y

And that's all there is to it. Once you get the hang of things it will be second-nature to you. You are welcome to continue browsing our site now, or you can read another lesson on the distributive property from AlgebraHelp or this lesson from Dr. Math.