Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3 • (k4)) -  (24•3k2)
 Step  2  :

Equation at the end of step  2  :

  3k4 -  (24•3k2)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   3k⁴ - 48k²  =   3k² • (k² - 16) 

Trying to factor as a Difference of Squares :

 4.2      Factoring:  k² - 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 :  k²  is the square of  k¹ 

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

Final result :

  3k2 • (k + 4) • (k - 4)