Module 8: Lesson 4

 

Self-Check 2

1. “Your Turn” from “Example 2” on page 541 of the textbook
   
   1. There are nine terms in the expansion of (2a − 7)8.
   2. The 4th term in the expansion of (2a − 7)8 can be found by using the binomial theorem.
      
      
       
      tk + 1 = nCk (x)n − k(y)k
      
      Four substitutions will need to be made.
      
      
       

      n = 8
      

       

      k = 3 (because it is the 4th term that is being looked for and the formula uses tk + 1)
      

       

      x = 2a
      

       

      y = −7
      
      After substitution, the equation is as follows:
      
      

       

      
      
      Solving the equation to completion results in the following answer:
      
      

       

      

   3. To determine the first four terms in the expansion of (3a + 2b)7, use the binomial theorem and the following information:
      
      

       

      n = 7
      

       

      x = 3a
      

       

      y = 2b

      
      
      

 

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