I just need this multiplied and 
simplified. The hashed line is 
supposed to be a solid line. 

 (4c² - 100)(16c + 48)
-----------------------
 (8c² - 72) (2c – 10) 

You don't multiply, you just factor everything 
and cancel!


Factor 4c² - 100
       4(c² - 25)
       4(c - 5)(c + 5)

Factor 16c + 48
       16(c + 3)

Factor 8c² - 72
       8(c² - 9)
       8(c - 3)(c + 3)

Factor 2c - 10
       2(c - 5)

Now replace each parentheses by its factorization:

       4(c - 5)(c + 5)16(c + 3)
      --------------------------
       8(c - 3)(c + 3)2(c - 5)

Multiply the 4 by the 16 in the top, getting 64
Multiply the 8 by the 2 in the bottom, getting 16

       64(c - 5)(c + 5)(c + 3)
      -------------------------
       16(c - 3)(c + 3)(c - 5)

Cancel the 16 into 64 and get 4 on top:

       4    
       64(c - 5)(c + 5)(c + 3)
      -------------------------
       16(c - 3)(c + 3)(c - 5)
       1

Cancel the (c - 5)'s

       4    1   
       64(c - 5)(c + 5)(c + 3)
      -------------------------
       16(c - 3)(c + 3)(c - 5)
       1                  1

Cancel the (c + 3)'s

       4    1             1  
       64(c - 5)(c + 5)(c + 3)
      -------------------------
       16(c - 3)(c + 3)(c - 5)
       1           1      1 

Now all that's left is

        4(c + 5)
       ---------
         c - 3
Edwin