Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (9 • (x2)) -  132y2
 Step  2  :

Equation at the end of step  2  :

  32x2 -  132y2

Step  3  :

Trying to factor as a Difference of Squares :

 3.1      Factoring:  9x²-169y² 

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 : 169 is the square of 13
Check :  x²  is the square of  x¹ 

Check :  y²  is the square of  y¹ 

Factorization is :       (3x + 13y)  •  (3x - 13y) 

Final result :

  (3x + 13y) • (3x - 13y)