Distributive property

Hi Manosh,

I'd like to give you some understanding of what the property is and why we use it.

First, think of a simple example. 3 x 7 = 21. But 7 can be decomposed into 2 + 5 so

3 x 7 = 3 x (2 + 5) = 21

In order for the equation to remain true, we have to be able to distribute the 3, or give him to each number in the parenthesis.

3 x (2 + 5) = 3 x 2 + 3 x 5 = 6 + 15 = 21.

When you're trying to understand something in math, always use a simple example to help you work through the concept.

Now, for your problem, you have

-2(-4 + 3c) – 2c = -2 x -4 + (-2)x3c - 2c

-2(-4 + 3c) – 2c = 8 - 6c - 2c

There are two kinds of terms here, numbers with c and numbers without a c. You can combine the numbers with a c. Think of it like this, the two terms with c have had a c distributed to them. So, we can factor out,
**or reverse distribute**, the c

-2(-4 + 3c) – 2c = 8 + c(-6 - 2) = 8 - 8c

But now, look at what we have, the two terms each have an 8 so we can reverse distribute the 8

-2(-4 + 3c) – 2c = 8(1 - c)

So factoring and distribution go hand in hand in our calculations! We call these inverse processes and if you have a good grasp on them, then your algebraic calculations will go more smoothly!