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  1.  
  2.                 Review of Algebraic Expressions and Exponents
  3.                 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
  4.  
  5. You MUST have all the following information at your fingertips at all times.
  6.  
  7.             You have NO CHANCE of passing calculus without it.
  8.   
  9.             
  10.                     (a + b) (c + d)   =   ac + ad + bc + bd
  11.  
  12.                                   2        2          2
  13.                            (a + b)    =   a  + 2ab + b 
  14.  
  15.                                            2
  16.                      (x - a) (x - b)  =   x  - (a + b)x + ab
  17.  
  18.                                            2    2
  19.                      (a - b) (a + b)  =   a  - b 
  20.  
  21.                         2         2        3    3
  22.               (a - b) (a  + ab + b )  =   a  - b 
  23.  
  24.  
  25. If a and b are positive integers:
  26.  
  27.                                  a b      a+b
  28.                                 x x   =  x 
  29.  
  30.  
  31.                              a
  32.                             x        a-b       1
  33.                            ────  =  x    =  ──────
  34.                              b                b-a
  35.                             x                x
  36.  
  37.                                a  b      ab
  38.                              (x )    =  x
  39.  
  40.                                   a      a a
  41.                               (xy)   =  x y
  42.  
  43.                                   a      a    a
  44.                              (x/y)   =  x  / y
  45.  
  46.  
  47.  
  48. ┌─────────────────┐
  49. │ Common Mistakes │
  50. └─────────────────┘
  51.  
  52. WRONG    - (x - y)  =  -x - y           RIGHT    - (x - y)  =  -x + y
  53.  
  54. WRONG     2(x + y)  =  2x + y           RIGHT     2(x + y)  =  2x + 2y
  55.  
  56.                  2      2         2                      2      2          2
  57. WRONG     (x + y)   =  x  + xy + y      RIGHT     (x + y)   =  x  + 2xy + y
  58.  
  59.                  2                                       2      2          2
  60. WRONG     (x - y)   =  (x - y)(x + y)   RIGHT     (x - y)   =  x  - 2xy + y
  61.  
  62.  
  63.               2 3       5                             2 3       6
  64. WRONG       (x )    =  x                RIGHT       (x )    =  x
  65.  
  66.              2  3       6                            2  3       5
  67. WRONG       x  x    =  x                RIGHT       x  x    =  x
  68.  
  69.  
  70. This is the end of the help file.  Press the ESC key to return to the quiz
  71. question you were doing.
  72.