Question 458813
<pre>
For the given function, find 

f(x+h) - f(x)
—————————————
      h


f(x) =  x² - 8x 
 
===================================================

To find

f(x+h) - f(x)
—————————————
      h

1.  First find f(x+h)

f(x) =  x² - 8x

That is, replace every x by (x+h), and get

f(x+h) = (x+h)² - 8(x+h)

Now simplify the right side:

f(x+h) = (x+h)(x+h) - 8x - 8h
f(x+h) = x² + hx + hx + h² - 8x - 8h
f(x+h) = x² + 2hx + h² - 8x - 8h

2. Now substitute x² + 2hx + h² - 8x - 8h for f(x+h) in

f(x+h) - f(x)
—————————————  
      h

and get

x² + 2hx + h² - 8x - 8h - f(x)
—————————————————————————————
              h

3. Now substitute (x² - 8x) for f(x) in that:

x² + 2hx + h² - 8x - 8h - (x² - 8x)
——————————————————————————————————
                h

Remove the parentheses in the numerator:

x² + 2hx + h² - 8x - 8h - x² + 8x
—————————————————————————————————
               h

Now the x² and the -x² cancel, and 
the -8x and the +8x cancel, giving:

2hx + h² - 8h
—————————————
      h

4. Now factor out h in the numerator:

h(2x + h - 8)
—————————————
      h

5. Now cancel the h factor in the numerator and
the denominator and get:

2x + h - 8

Now if you will swap the last two terms you will
get choice A). 

A) 2x - 8 + h 
 
Edwin</pre>