ADVANCED EXERCISES

(1) Simplify the following expressions. 


 (a) 

 (b) |2| - |p + |p -|-p| - p| + |-2||
SOLUTION: 

 (a) 

     = 

     = |a + b|

     
 (b) |2| - |p + |p - |-p| - p| + |-2||

      = 2 - |p + |p - |p| - p| + 2|

      = 2 - |p + |-|p|| + 2|

      = 2 - |p + |p| + 2|

      = 2 - |p - p + 2| = 2 - |2| = 2 - 2 = 0 if p < 0

      or 
      = 2 - |p + p + 2| = 2 - |2p+2| = 2 - 2p - 2 = -2p  if p 0

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