Simplify
Simplify: to make simpler!
One of the big jobs we do in Algebra is "simplification".
You will often get asked to express something "in simplest form".
What is the Simplest Form?
In general, it is simpler if it is easier to use.
And:
Example
This:  2w(5wy)  
can become this:  10w^{2}y  (by multiplying the constants and variables) 
and it is easier to use.
And:
This: 


can become this: 

(by polynomial long division) 
And:
This:  x^{2}  2x  3  
can become this:  (x3)(x+1)  (by factoring) 
That last example might be controversial ... some people say that you should remove parentheses to make it "simpler", but (x3)(x+1) is usually a lot easier to use.
The moral of the story:
"Simplified" is sometimes obvious, but can also depend on what you want to do!
How to Simplify
Simplifying uses much the same skills as solving equations, that page has some good advice.
But here is a small list of tips:
 Combine Like Terms
 Factoring
 Expanding (the opposite of factoring) can also sometimes help
 Clear out fractions by multiplying
 Recognizing a pattern you have seen before, like the difference of squares
And Which Is Simpler Here?
Here is one more interesting case:
This:  seems simple enough  
But this:  has a rationalized denominator (normally considered simpler, and preferred by teachers!) 
Which is simpler? You decide!