Review 1 Problems Only Algebra B
SOLUTIONS
1a  1b   2a  2b  2c   3a   3b

     1a)

                                Simply this fraction.


     ANSWER
     When you divide powers to the same base (y in this problem), use the exponent rule
     that you always subtract the bottom exponent (35) from the top exponent (20),
     so the answer is

                                  

   or

                                   

    or

    writing your answer with positive exponents only, use the definition of negative exponents
    as being reciprocals, so

                               

           is the answer

     1b) 
                          Work out this product raised to a power.



     ANSWER
     You have a product raised to a power, so you use the rule that you must raise each factor
                                                          in the product to that power

                                                       

               

      Using positive exponents only, the answer is  
                                                                                              

      The positive exponent stays on the top where it was, but the negative exponents go to the bottom,
     because negative exponents mean reciprocals, and become positive exponents when you write them
     on the bottom. The exponent 21 stays 21 on the top, but the exponents   -12   and   -18   become positive
     12  and   positive 18   when you write on the bottom.

 

     2a)

                       Do the multiplication and simplify your answer.

      ANSWER
     Whenever you multiply, you use the distributive rule.
     You multiply everything in one parenthesis by everything in the other parenthesis.

          

    

    

                                                                              is the answer.

                                                                     There are no like terms to combine so this is the final answer.

     2b)
              
 
                                                                        Multiply and simplify your answer. When possible,
                                                                       simplify the square roots.
                                                                         y means y times the square of three.
                                                                            is not an exponent here although its placement
                                                                        by the HTML code makes it appear to be an exponent.


    ANSWER
    You should recognize that you should use the identity

                                       Difference of Two Square

                                                                       
                                       to work the problem.

     You must identify terms in the problem with the terms in the identity you want to use in order
      to be able to use the identity. If you can not make the appropriate identifications, then you can
     not use the identity and you have to find another tentative identity that you may be able to use
     in working out the problem.
     In this problem you can identity
              and     

     so the problem exactly fits the form of the identity Difference of Two Squares.

                        
                       is the answer.

                     Remember that
                                                        .


     2c)
                                        Do the multiplication by using the identity
                                                                        Square of a Difference

                                                                                        
                                                                        Be sure to simply your answer by working out the square roots.


     ANSWER

     

                                                           is the answer.

     3a)
         Factor Completely
                                                  


     ANSWER
     First, you use the Distributive Law
                                                                  

     to factor out the    7  , so you get

           

    and then you notice that

                 

     is of the form Difference of Two Squares, because you can write               

               

     so

               

             

     You can do Difference of Two Squares again because

              

     so


     

     But      is again in the form Difference of Two Squares, so you can use the identity again

                

      

   is the final answer.

    Remember that the original problem had a factor   7  in front of the parenthesis, so you put it back in
    to write down the final answer to the problem.

     This problem points out the important fact that you can use a rule or a law or an identity   -   in this case
    the Difference of Two Squares identity   -   as often as necessary to work out a problem.
    Remember that!!

      3b)
           Factor completely
                                                   

   ANSWER
    The coefficient, that is, the number in front of the      is   1   so you can use the simple method
     where you find two numbers whose sum is   4   and whose product is    -21.
    -3   and    7   satisfy those requirements, so

                                                            is the final answer


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