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 = (4 + 5)c or ...
4c -  5c = (4 -  5)c = - c
The opposite is also true:
(a + b)c = ac + bc
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, 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: 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