Question

multiply the binomials:
x-2y and 2x-y

Answer 1

Step  1  :

Equation at the end of step  1  :

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

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3x2 - 3xy + 3y2  =   3 • (x2 - xy + y2) 

Trying to factor a multi variable polynomial :

 3.2    Factoring    x2 - xy + y2 

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

 Factorization fails

Equation at the end of step  3  :

(x - 2y) + 3 • (2x - y) • (x2 - xy + y2)

Step  4  :

Trying to factor by pulling out :

 4.1      Factoring:  6x3-9x2y+9xy2+x-3y3-2y 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  6x3+x 
Group 2:  -9x2y+9xy2 
Group 3:  -3y3-2y 

Pull out from each group separately :

Group 1:   (6x2+1) • (x)
Group 2:   (x-y) • (-9xy)
Group 3:   (3y2+2) • (-y)


Looking for common sub-expressions : 

Group 1:   (6x2+1) • (x)
Group 3:   (3y2+2) • (-y)
Group 2:   (x-y) • (-9xy)

Bad news !! Factoring by pulling out fails : 

The groups have no common factor and can not be added up to form a multiplication.

Final result :

6x3 - 9x2y + 9xy2 + x - 3y3 - 2y

Answer 2

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