Question

Simplify (x-2y) 3 -(2x-y) 3

Answer 1

The given expression is in the form of  a³ - b³ = ( a - b) (a² + ab + b²)
So we get
[ (x-2y) - (2x-y) ] [ (x-2y)² + (x-2y)(2x-y) + (2x-y)² ]
    = - (x + y) [ 7 x² + 7 y² - 13 x y ]

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(x - 2 y)³ - (2 x - y)³ 
  = x³ - 8 y³ - 6 x² y + 12 x y² - [8 x³ - y³ - 12 x² y + 6 x y² ]
  = - 7 x³ - 7 y³ + 6 x² y + 6 x y²
  

Answer 2

(x - 2 y)³ - (2 x - y)³ 
  = x³ - 8 y³ - 6 x² y + 12 x y² - [8 x³ - y³ - 12 x² y + 6 x y² ]
  = - 7 x³ - 7 y³ + 6 x² y + 6 x y²