Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  81 -  72v2

Step  2  :

Trying to factor as a Difference of Squares :

 2.1      Factoring:  81-49v² 

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 :  81  is the square of  9 
Check : 49 is the square of 7
Check :  v²  is the square of  v¹ 

Factorization is :       (9 + 7v)  •  (9 - 7v) 

Final result :

  (7v + 9) • (9 - 7v)