Solution - Factoring multivariable polynomials

Step  1  :

Equation at the end of step  1  :

  ((2 • (r2)) +  8rs) -  (2•3•7s2)
 Step  2  :

Equation at the end of step  2  :

  (2r2 +  8rs) -  (2•3•7s2)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   2r² + 8rs - 42s²  =   2 • (r² + 4rs - 21s²) 

Trying to factor a multi variable polynomial :

 4.2    Factoring    r² + 4rs - 21s² 

Try to factor this multi-variable trinomial using trial and error 

 Found a factorization  :  (r + 7s)•(r - 3s)

Final result :

  2 • (r + 7s) • (r - 3s)