Question 903107
Ok, let's take a look at the equation

n + n (n- 3)

For the part  n (n +3) , we can express this using the Distributive Postulate. A postulate is a statement that is true. The Distributive method is as follows:

a (b + c) = ab + ac

We take the 'a' and multiply it with the 'b' which gives us ab plus the 'a' multiplied by the 'c,' which gives us ac

So, n + n ( n-3) = n + n ^ 2 - 3n = n^2 - 2n = n (n -2)

It will not simplify to n (n-1) . 

" One item I should have asked about this expression.  If the simplified expression n(n-2) is put over denominator of 2, would this then simplify to n(n-1)  ??"

The answer is no. Here's why. You can only cancel factors , not terms in a polynomial. Let me explain .

2n/2 * n/2 =  n^2/2    Correct 

(2n + 5)/ 2 = n + 5    Incorrect ( You cannot cancel the 2's and get n+5)

So, for  [n(n-2)]/2 , your answer would still be [n(n-2])/2 because there are no factors to cancel.

You can alternately do this:

[n(n-2)]/2 = (n^2-2n)/2= n^2/2 -2n/2 =  n^2/2 - n 

You are getting rid of the parenthesis and then putting each term over the same denominator.  The two terms are n^2 and -2n . You put each over the denominator  2. Then you can reduce each separate fraction where applicable.However, it does make things more complicated. This topic comes under
'simplifying rational expressions."