Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2•3•52k2) -  216

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   150k² - 216  =   6 • (25k² - 36) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  25k² - 36 

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 :  25  is the square of  5 
Check : 36 is the square of 6
Check :  k²  is the square of  k¹ 

Factorization is :       (5k + 6)  •  (5k - 6) 

Final result :

  6 • (5k + 6) • (5k - 6)