Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "l2"   was replaced by   "l^2". 

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   mas² - ac²l²  =   a • (ms² - c²l²) 

Trying to factor as a Difference of Squares :

 2.2      Factoring:  ms² - c²l² 

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 :  m¹   is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares

Final result :

  a • (ms2 - c2l2)