Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3 • (x4)) -  (24•3x2)
 Step  2  :

Equation at the end of step  2  :

  3x4 -  (24•3x2)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   3x⁴ - 48x²  =   3x² • (x² - 16) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  x² - 16 

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 : 16 is the square of 4
Check :  x²  is the square of  x¹ 

Factorization is :       (x + 4)  •  (x - 4) 

Final result :

  3x2 • (x + 4) • (x - 4)