Question

(x+2y) (-3x-y)-(x+y) (x-y) +(x-2y) (-2x+y)

Answer 1

(x+2y)(-3x-y)-(x+y)(x-y)+(x-2y)(-2x+y) 

Final result :

-6x2 - 2xy - 3y2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

(((x+2y)•(-3x-y))-((x+y)•(x-y)))+(x-2y)•(y-2x)

Step  2  :

Equation at the end of step  2  :

(((x+2y)•(-3x-y))-(x+y)•(x-y))+(x-2y)•(y-2x)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -3x - y  =   -1 • (3x + y) 

Equation at the end of step  4  :

((-x-2y)•(3x+y)-(x+y)•(x-y))+(x-2y)•(y-2x)

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -6x2 - 2xy - 3y2  =   -1 • (6x2 + 2xy + 3y2) 

Trying to factor a multi variable polynomial :

 6.2    Factoring    6x2 + 2xy + 3y2 

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

 Factorization fails

Final result :

-6x2 - 2xy - 3y2