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.


This:   5x + x - 3    
can become this:   6x - 3   (by combining like terms)

and it is easier to use.



This:   2w(5wy)    
can become this:   10w2y   (by multiplying the constants and variables)

and it is easier to use.


2x2 - 6x + 2
x - 3
can become this:  
2x + 2
x - 3
  (by polynomial long division)


This:   x2 - 2x - 3    
can become this:   (x-3)(x+1)   (by factoring)

That last example might be controversial ... some people say that you should remove parentheses to make it "simpler", but (x-3)(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:

And Which Is Simpler Here?

Here is one more interesting case:

This:   1/sqrt2   seems simple enough
But this:   sqrt2/2   has a rationalized denominator
(normally considered simpler, and preferred by teachers!)

Which is simpler? You decide!