Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "r1"   was replaced by   "r^1". 

Step  1  :

Trying to factor as a Difference of Squares :

 1.1      Factoring:  v-r¹⁰⁰a 

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 :  v¹   is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares

Final result :

  v - r100a