
                Review of Algebraic Expressions and Exponents
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You MUST have all the following information at your fingertips at all times.

            You have NO CHANCE of passing calculus without it.
  
            
                    (a + b) (c + d)   =   ac + ad + bc + bd

                                  2        2          2
                           (a + b)    =   a  + 2ab + b 

                                           2
                     (x - a) (x - b)  =   x  - (a + b)x + ab

                                           2    2
                     (a - b) (a + b)  =   a  - b 

                        2         2        3    3
              (a - b) (a  + ab + b )  =   a  - b 


If a and b are positive integers:

                                 a b      a+b
                                x x   =  x 


                             a
                            x        a-b       1
                           ────  =  x    =  ──────
                             b                b-a
                            x                x

                               a  b      ab
                             (x )    =  x

                                  a      a a
                              (xy)   =  x y

                                  a      a    a
                             (x/y)   =  x  / y



┌─────────────────┐
│ Common Mistakes │
└─────────────────┘

WRONG    - (x - y)  =  -x - y           RIGHT    - (x - y)  =  -x + y

WRONG     2(x + y)  =  2x + y           RIGHT     2(x + y)  =  2x + 2y

                 2      2         2                      2      2          2
WRONG     (x + y)   =  x  + xy + y      RIGHT     (x + y)   =  x  + 2xy + y

                 2                                       2      2          2
WRONG     (x - y)   =  (x - y)(x + y)   RIGHT     (x - y)   =  x  - 2xy + y


              2 3       5                             2 3       6
WRONG       (x )    =  x                RIGHT       (x )    =  x

             2  3       6                            2  3       5
WRONG       x  x    =  x                RIGHT       x  x    =  x


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