## Distributive property

The distributive property of algebra is about grouping terms.
It states that for any real numbers a, b, and c, that :

 ac + bc = (a + b)c or ... ac -  bc = (a - b)c
So, using a = 4 and b = 5:
 4c + 5c = (4 + 5) c or ... 9c 4c -   5c = (4 -   5) c = - c

The opposite is also true:
(a + b) c = ac + bc

Also, if you have terms in parentheses that are multiplied by other terms in parentheses, like this:
(a + b) (c + d)
then each term in the first parenthesis is multiplied by each term in the second, like this:
(a + b) (c + d) = ac + ad + bc + bd
Basically what this property means is that if two or more terms involve the same variable (say "c"), and they are either added or subtracted (not multiplied or divided), then you can group the other terms together inside parentheses and multiply the whole term in the parentheses times c. This often lets you simplify an expression by combining the terms inside the parentheses. Here's an example:

 1. Start with this expression: 4ac - 2bc + 3ac + 5bc 2. All terms involve c, so we have : (4a - 2b + 3a + 5b) c 3. We can group the a and b terms also: ((4 + 3)a + (-2 + 5)b) c 4. Now simplify: ( 7a + 3b ) c