Module 8: Lesson 4

 

Self-Check 2

2. Questions 3.b., 11.c., 12.a., 12.b., 17.a., and 17.d. on pages 542 to 543
   3.  
      2. This is the 4th term in row 7 of Pascal’s triangle, which means that it will be equivalent to 6C3 or
   11.  
       3. You will probably use a method such as guess and test to solve this question. By using this method, you should notice that the value of r that gives the maximum value occurs when r = 6. The value for 12C6 is 924.
   12.  
       1. By looking at the expansion, you can see the following for the binomial (a + b)n:
          
          
           

          n = 4
          

           

          a = x
          

           

          b = y
          
          Thus, this expansion is equivalent to (x + y)4.

       2. By looking at the expansion, you can see the following for the binomial (a + b)n:
          
          
           

          n = 5
          

           

          a = 1
          

           

          b = −y
          
          Thus, this expansion is equivalent to (1 − y)5.

   17.  
       1. The following information is necessary to solve this question:
          
          
           
          n = 3
          
           
          k = 0 or 1 or 2 or 3 (depending on which term is being solved for)
          
           
          
          
           
          y = 2
          
          The solution for the first four terms (all of the terms) is as follows:
          
          
          
          Thus, the expansion of the first four terms is
       4. Before solving this question, it may be easier to arrange it so that there are no fractions.
          
          
           
          
          
          

          The following information is necessary:
          
          

           

          n = 4
          

           

          k = 0 or 1 or 2 or 3 or 4 (depending on which term is being solved for)
          

           

          x = 2x2
          

           

          y = −x−1
          
          

          The solution for the first five terms (which is all of the terms) is as follows:
          
          

          
          
          
          

          Thus, the expansion of the first five terms is 16x8 − 32x5 + 24x2 − 8x−1 + x−4 or

 

 

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