INTRODUCTORY EXERCISES - Symbol Manipulation

(1) Simplify. Expand any products.

 (a) 4y - (6 - 3x + y)

 (b) (2 + 13/3)(9/52)
              
 (c) (4/x)-1  

 (d) 3 - (1/2)(-x2 + x + 2) - 5(1.2x2 - 2.7)

 (e) 2r2 + 4(2r)(100/r2)

 (f) -36(x - 1)(x + 2)

 (a)  4y - (6 - 3x + y)
      4y - 6 + 3x - y
      3y - 6 + 3x
      3y + 3x - 6

 (b) (2 + 13/3)(9/52)
     ( 2(3)/3 + 13/3 )(9/52)  --common denominator of 3
     (6/3 + 13/3)(9/52)
     (19/3)(9/52)
     (19)(3)/(52)   --in the step above, a common factor of 3 can be cancelled
                       from the numerator and denominator
     
 (c) (4/x)-1

       1         1         x
     -----  =  -----   =  ---
     (4/x)1    (4/x)       4

     
 (d)  3 - (1/2)(-x2 + x + 2) - 5(1.2x2 - 2.7)
      3 + (x2/2) - (x/2) - (2/2) - 5(12/10)x2 + 5(27/10)
      3 + (x2/2) - (x/2) - 1 -(60/10)x2 + (27/2)

      x2 - 60x2  -  x   + 3 - 1 + 27
     ---   ----    ---           ---
      2     10      2             2

     x2 - 12x2  -  x  +  6  -  2  + 27    ---find common denominators
     ---  ----   ---   ---   ---  ---       
      2    2      2     2     2    2  

    -55x2 -  x  +  31
    -----   ---   ---
     10      2     2

    -11x2 -  x  +  31
    -----   ---   ---
      2      2     2    


 (e) 2r2 + 4(2r)(100/r2)
     2r2 + 4(2)(100/r)    ---cancel common factor of  2r from both
                                          numerator and denominator
     2r2 + (800/r)
     
     2r3 + 800         ---find common denominator
     ----   ---
      r      r
      
     2r3 + 800
     ----------
         r

 (f) (2x - 1)2 = (2x - 1) (2x - 1) = 22x2 - 2x  - 2x + 1
     = 4x2 - 4x +1