Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

      ((22x2 - 7)4) 
  3 • —————————————
            3      

Step  2  :

            (4x2 - 7)4
 Simplify   ——————————
                3     

Trying to factor as a Difference of Squares :

 2.1      Factoring:  4x² - 7 

Put the exponent aside, try to factor  4x²-7 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  4  is the square of  2 
Check : 7 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  2  :

      (4x2 - 7)4
  3 • ——————————
          3     

Step  3  :

Final result :

  (4x2 - 7)4