SOLUTION: Can these be factored using the methods (GCF, squares, cubes) a4 + 1 a4

SOLUTION: Can these be factored using the methods (GCF, squares, cubes) a4 + 1 a4 - 64

Question 1184738: Can these be factored using the methods (GCF, squares, cubes)
a4 + 1
a4 - 64
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.
Can these be factored using the methods (GCF, squares, cubes)
(a) a4 + 1
(b) a4 - 64
~~~~~~~~~~~~~~~

(b)  a^4 - 64  can be factored this classic way

          = 

    over integer numbers.


    It can be factored further as

          =  =  = 

    but just over real numbers, not over integer or rational numbers.


    The factor   can be factored further over COMPLEX numbers.




(a)    can be factored in this way

          =  -  =  -  = 

               = .


     This factoring works over real numbers and includes the irrational number .

     It does not work over integer or rational numbers.

Solved, answered and explained.

----------------

See the lesson
- Advanced factoring
in this site.

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