Distributing and combining like terms is very useful.

Lets say you have 5 + 3 = 0.

When you combine like terms, you add all the like terms to their counterparts, so in this case, 5 and 3.

So it is now 8 = 0.

A more complicated example:

Lets say you have 5y + 3x + 8y + 5x = 2.

You have to combine all like terms, so you combine 5y and 8y to get one value of y, and 3x and 5x to get one value of x.

So 13y + 8x = 2.

Now, distributing.

Distributing is also known as factoring. It's when you put a group of numerical properties (numbers or variables) into a more simplified group multiplied by a common factor (preferrably the greatest common factor).

Take 3x + 3 = 0.

Now just take the left handed side.

The greatest common factor for 3x + 3 is 3.

So, you can do this: 3 * (x + 1).

As you can see, this expression turns out to be 3x + 3.

You can also do it the other way around to further simplify an expression.

If you have 4(x - 1) = 0

You can evaluate that to be 4x - 4 = 0.