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Solution - Simplification or other simple results

8m275
8m^27-5

Step by Step Solution

Step  1  :

Equation at the end of step  1  :

  (23m26 • m) -  5

Step  2  :

Trying to factor as a Difference of Cubes:

 2.1      Factoring:  8m27-5 

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into
              (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =
            a3+a2b+ab2-ba2-b2a-b3 =
            a3+(a2b-ba2)+(ab2-b2a)-b3 =
            a3+0+0-b3 =
            a3-b3


Check :  8  is the cube of  2 

Check :  5  is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  8m27 - 5

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