Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2". 

Step  1  :

Equation at the end of step  1  :

  (26•3x2) -  243

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   192x² - 243  =   3 • (64x² - 81) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  64x² - 81 

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 :  64  is the square of  8 
Check : 81 is the square of 9
Check :  x²  is the square of  x¹ 

Factorization is :       (8x + 9)  •  (8x - 9) 

Final result :

  3 • (8x + 9) • (8x - 9)