Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22•3n2) -  27

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   12n² - 27  =   3 • (4n² - 9) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  4n² - 9 

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 : 9 is the square of 3
Check :  n²  is the square of  n¹ 

Factorization is :       (2n + 3)  •  (2n - 3) 

Final result :

  3 • (2n + 3) • (2n - 3)