Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  34x2 -  9

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   81x² - 9  =   9 • (9x² - 1) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  9x² - 1 

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 :  9  is the square of  3 
Check : 1 is the square of 1
Check :  x²  is the square of  x¹ 

Factorization is :       (3x + 1)  •  (3x - 1) 

Final result :

  9 • (3x + 1) • (3x - 1)