Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (6 • (x2)) -  24y2
 Step  2  :

Equation at the end of step  2  :

  (2•3x2) -  24y2

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   6x² - 16y²  =   2 • (3x² - 8y²) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  3x² - 8y² 

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 :  3  is not a square !!

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

Final result :

  2 • (3x2 - 8y2)